MSBSHSE Syllabus for Class 12 Logic (Logic 2020)

What the 2020 Class 12 Logic Syllabus Contains

The 2020 Logic syllabus is the official document issued by the state board for the Higher Secondary Certificate (HSC) Logic paper. It does three jobs: it names the seven units of the course, it breaks each unit into sub-topics, and it states the learning outcomes expected of you at the end of each unit. A learning outcome is a sentence describing what you should be able to do, for example "construct a truth table for a compound proposition" rather than simply "know truth tables".

This syllabus applies to Arts stream students who appeared for the Class 12 exam in 2020, or who are studying from the 2020 edition of the textbook. It is published in both English and Marathi medium. The units, sub-topics and outcomes are identical in both; only the language of the textbook and the paper differs, so a Marathi-medium student and an English-medium student prepare exactly the same content.

The most useful way to read it is as a boundary document, not a contents page. The list of units tells you what exists; the sub-topics tell you how deep you must go. For instance, if a sub-topic says "truth tables for two and three variables", a two-variable example is enough and you are not expected to build five-variable tables. Before you leave out any sub-topic as unimportant, check it against the outcomes listed beside it. If you are also planning your other papers, the Class 12 syllabus hub for the 2020 academic year lists every subject in one place.

Unit-Wise Structure and Approximate Marks

The Logic course has seven units, and each unit corresponds to one chapter of your textbook. The order below is the order in which the topics build on each other, so do not skip ahead: Decision Procedure and Deductive Proof give you the tools that Predicate Logic then extends, and Traditional Logic sets up the vocabulary that Syllogism uses.

Treat the weight column as a rough guide only. Not every edition of the syllabus prints a unit-wise marks split, and where a figure does appear it is indicative rather than a promise about the question paper. [verify] Your teacher, who has seen previous papers, is the better judge of which chapters repeat every year.

The overall split follows the general HSC pattern for Arts subjects: the written theory paper carries 80 marks and the remaining 20 marks come from internal assessment, either a project or an oral. [verify] That means the written paper is still where most of your marks are decided, so a chapter being "small" is no reason to leave it.

Do not assume all seven units carry equal marks. Traditional Logic and Syllogism are the foundation of the paper and usually attract more questions, including the longer answers, because they test rules you can apply and mark reliably. [verify] A sensible revision plan gives these two chapters more written practice, while Predicate Logic and Hypothesis may need more reading time before practice.

Use the table to plan, not to gamble. If you have ten days left, spend the largest share on the two high-weight chapters, a fixed daily slot on truth tables and proofs so the skill stays sharp, and the rest on the conceptual chapters. For worked answers to the exercises in each of these seven chapters, see the Class 12 Logic textbook chapter-wise solutions.

Chapter 1: Decision Procedure

A decision procedure is a fixed, mechanical method that tells you, in a finite number of steps, whether a proposition or an argument form is valid. "Mechanical" is the key word: you do not need insight or intuition, you follow steps and the answer comes out the same for everyone. In this chapter that method is the truth table.

Start with the five truth functions and their tables: negation (not), conjunction (and), disjunction (or), conditional (if...then) and biconditional (if and only if). Learn the column for each by heart, especially the conditional, which is false only when the antecedent is true and the consequent is false. Then move to compound propositions with two and three variables. A two-variable proposition needs 4 rows, a three-variable one needs 8 rows, and the number doubles with each extra variable.

A typical exam question gives you a form such as [(P → Q) ∧ P] → Q and asks you to test it with a truth table. Marks are usually given for the correct number of rows, correct sub-columns for each part of the formula, and a clear final statement of whether the form is a tautology, a contradiction or contingent. [verify]

If your textbook also covers a shorter method, such as the reductio (indirect) test or the truth-tree method, learn where it differs from the full table. The full table always works but is slow for three or more variables; the shorter method tries to find one row where the premises are true and the conclusion false, and if no such row can exist, the form is valid.

The most common mistake is confusing "valid" with "true". A decision procedure tests the form of an argument, not the factual content of its sentences. "If it rains, the ground is wet; it rains; therefore the ground is wet" and "If cats fly, the moon is cheese; cats fly; therefore the moon is cheese" have the same valid form, even though the second has false premises. The fix is simple: before you start, replace the sentences with letters (P, Q, R) and work only with the letters. For worked truth tables from this chapter, see the Class 12 Logic textbook chapter-wise solutions.

Chapter 2: Deductive Proof

A proof is a numbered list of steps. Line 1 is a premise, the last line is the conclusion you want, and every line in between follows from the lines above it by a named rule. The rule name written on the right is called the justification, and it is not optional. A line without a justification earns nothing, even if the formula on it is correct.

The rules you need fall into two groups. Rules of inference let you pull out a new line from existing lines: modus ponens (from P → Q and P, get Q), modus tollens (from P → Q and not-Q, get not-P), disjunctive syllogism (from P ∨ Q and not-P, get Q), hypothetical syllogism (from P → Q and Q → R, get P → R) and constructive dilemma. Replacement rules let you swap one formula for a logically equivalent one anywhere inside a line: De Morgan's laws, double negation, commutation, association, distribution, exportation, transposition and material implication. The difference matters: inference rules work on whole lines, replacement rules work on parts of a formula.

A typical exam question gives three or four premises and a conclusion, and asks for a formal proof. Marks usually go for the correct sequence of steps, the right rule named at each step, and the conclusion actually reached in the form asked. [verify]

Take premises 1. P → Q, 2. Q → R, 3. P, and prove R. Line 4 is P → R by hypothetical syllogism on 1 and 2. Line 5 is R by modus ponens on 4 and 3. Two lines, two justifications, done.

A direct proof moves forward from premises to conclusion. An indirect proof (reductio ad absurdum) adds the negation of the conclusion as an assumed premise, derives a contradiction such as S ∧ ~S, and then concludes that the original conclusion must be true. In an indirect proof, mark the assumed premise clearly, for example with "AP" for assumed premise, so the examiner can see where the assumption starts and ends.

The most common mistake is applying a rule to the wrong part of a formula, or skipping a justification line. The fix: after writing each line, point at the exact earlier lines the rule used and check the symbols match, then write the rule name before moving on. For solved proofs step by step, see the Class 12 Logic textbook chapter-wise solutions, and for proof-based questions from past papers, work through the Class 12 Logic previous year question papers.

Chapter 3: Predicate Logic

Propositional logic treats "Ram is tall" as a single letter, P. That is fine until you need to say "all men are mortal" or "some students passed", where the meaning depends on how many things have a property. Predicate logic breaks a sentence into parts: the subject (Ram, students), the property or relation (tall, passed) and a quantifier that says how much of the subject is covered.

Two quantifiers do all the work. The universal quantifier ∀ is read "for all" or "for every", and the existential quantifier ∃ is read "there exists at least one" or "for some". With a variable x and a predicate M(x) meaning "x is mortal", the sentence "all men are mortal" becomes ∀x (M(x) → Mortal(x)), and "some men are wise" becomes ∃x (M(x) ∧ Wise(x)).

Notice the connectives. Universal statements take →, existential statements take ∧. Writing ∀x (M(x) ∧ Mortal(x)) says everything in the world is a mortal man, which is not what you meant. This mix-up is a standard exam trap.

Every quantifier has a scope: the part of the formula it governs, usually shown by brackets. A variable inside the scope of its quantifier is bound; a variable outside any quantifier that binds it is free. A formula with no free variables is a closed formula, and only closed formulas can be true or false.

Proofs in predicate logic add four rules to the propositional ones you already know: universal instantiation (drop ∀ and put a name or variable in its place), universal generalisation, existential instantiation and existential generalisation. A typical question gives premises such as ∀x (P(x) → Q(x)) and P(a), and asks you to derive Q(a): instantiate the first premise to P(a) → Q(a), then apply modus ponens to get Q(a). Marks go for naming the quantifier rule at each step. [verify]

Nested quantifiers change meaning with order. "For every x there is some y such that x loves y" (∀x ∃y L(x, y)) means everyone loves somebody. Swap them to ∃y ∀x L(x, y) and it means there is one person whom everyone loves. Same symbols, different claim. Before translating or proving, read the sentence aloud and fix the order first.

For worked translations and quantifier proofs, use the Class 12 Logic textbook chapter-wise solutions, and for past exam questions on this chapter, see the Class 12 Logic previous year question papers.

Chapter 4: Traditional Logic

Traditional logic deals with categorical propositions: statements that relate two classes or categories. Every categorical proposition has four parts: a quantifier (All, No, Some), a subject term, a copula (is/are), and a predicate term. The four standard forms are named with vowels:

• A (universal affirmative): All S are P. Example: All poets are imaginative.
• E (universal negative): No S are P. Example: No poets are lazy.
• I (particular affirmative): Some S are P. Example: Some poets are rich.
• O (particular negative): Some S are not P. Example: Some poets are not rich.

Distribution of terms is the concept examiners test most. A term is distributed when the proposition says something about every member of that class. In A, only the subject is distributed. In E, both terms are distributed. In I, neither is distributed. In O, only the predicate is distributed. A quick way to remember: universal propositions distribute the subject, negative propositions distribute the predicate.

The square of opposition shows how the four forms relate when they share the same subject and predicate. A and O are contradictories: exactly one is true. E and I are also contradictories. A and E are contraries: they cannot both be true, but they can both be false. I and O are subcontraries: they cannot both be false, but they can both be true. A and I, and E and O, are subalterns: if the universal is true, the particular below it is true.

The common mistake here: students see that "All poets are imaginative" is false and conclude "No poets are imaginative" must be true. That is wrong. Both contraries can be false at the same time, for instance if some poets are imaginative and some are not. The fix is to test with a middle case before deciding.

Conversion swaps subject and predicate. E and I convert simply (No S are P becomes No P are S; Some S are P becomes Some P are S). A converts only by limitation, to an I proposition. O does not convert. Obversion changes the quality and replaces the predicate with its complement, and it is valid for all four forms. Contraposition combines obversion and conversion, and works fully for A and O.

Mood and figure belong to syllogisms, but the identification skill starts here. The mood is the three letters of the premises and conclusion in order (for example, AAA or EIO), and the figure depends on where the middle term sits in each premise. A typical exam question gives a syllogism and asks for its mood and figure, with marks split between the two answers. [verify]

For solved exercises on the square of opposition and conversion, use the Class 12 Logic textbook chapter-wise solutions.

Chapter 5: Syllogism

A categorical syllogism is an argument with exactly two premises and one conclusion, all of them categorical propositions, sharing three terms. The major term is the predicate of the conclusion, the minor term is the subject of the conclusion, and the middle term appears in both premises but never in the conclusion. The premise containing the major term is the major premise; the one containing the minor term is the minor premise.

Textbook example: "All mammals are warm-blooded. All whales are mammals. Therefore all whales are warm-blooded." Major term: warm-blooded. Minor term: whales. Middle term: mammals. The mood is AAA and the figure is the first, because the middle term is the subject of the major premise and the predicate of the minor. Exam questions usually give you a syllogism and ask for mood, figure and validity, with marks split across the three parts. [verify]

You have two routes to testing validity. The first is memorising the valid moods for each of the four figures. The second, safer route is learning the general rules: the middle term must be distributed at least once, no term may be distributed in the conclusion if it was undistributed in the premise, and no conclusion can be negative if both premises are affirmative (and if one premise is negative, the conclusion must be negative).

Each rule broken gives a named fallacy:

• Undistributed middle: the middle term is never distributed, so the premises fail to link the subject and predicate classes.
• Illicit major: the major term is distributed in the conclusion but not in the major premise.
• Illicit minor: the same error with the minor term.
• Four terms: the middle term shifts meaning between the two premises, so the argument really has four terms, not three.

Venn diagrams give you a fast check. Draw three overlapping circles for the three terms, shade the areas the premises rule out, and see whether the conclusion's claim is already shown. If it is, the form is valid. This takes under a minute once you have practised a dozen examples, which is why it is worth using in the exam before you commit to an answer.

The common mistake: students read the premises, decide they sound true, and mark the syllogism valid. Validity depends only on form. "All cats are birds. All birds are fish. Therefore all cats are fish" is valid, even though every statement in it is false. The fix is to strip the content and test the structure, using the rules or a Venn diagram. For practice sets with worked answers, see the Class 12 Logic textbook chapter-wise solutions and the previous year question papers.

Chapter 6: Grounds of Induction

Deduction and induction are two different directions of reasoning, and the exam expects you to state the difference in one clean sentence. Deduction moves from a general rule to a particular case: "All metals expand on heating; copper is a metal; therefore copper expands on heating." If the premises are true, the conclusion must be true. Induction moves the other way, from observed particulars to a general claim: "This iron rod expanded, this copper rod expanded, this brass rod expanded; therefore all metals expand on heating." The conclusion goes beyond what you have actually seen, so it can only be probable.

Mills methods are the five ways of arguing from observed cases to a cause. Learn each by its question:

• Method of agreement: several cases share only one circumstance before the effect, so that circumstance is the cause. Example: five students fall ill after a picnic, and the only food all five ate was the same sweet.
• Method of difference: two cases are alike except for one circumstance, and the effect appears only where that circumstance is present.
• Joint method of agreement and difference: the first two methods used together, one set of cases agreeing and another set differing.
• Concomitant variation: as one circumstance changes in degree, the effect changes correspondingly, for example the more a spring is stretched, the longer it becomes.
• Method of residues: subtract from the effect the parts already explained by known causes, and the remainder is attributed to the unknown cause.

A typical exam question gives you a short passage and asks which method is used and why. Marks are usually split between naming the method and justifying it from the wording of the passage, so quote the part of the passage that shows the pattern. For worked examples of this type, see the Class 12 Logic textbook chapter-wise solutions.

The problem of induction is the question of justification: past regularity does not guarantee future regularity, so an inductive conclusion is always probable, never certain. One counter-example can overturn a generalisation built from a thousand confirmations. The common mistake is treating an inductive conclusion as a deductive certainty, writing "therefore it must be so" when the honest phrasing is "therefore it is likely that". The fix is to check the direction of the argument first: if the conclusion is broader than the evidence, the word "must" does not belong in your answer.

Chapter 7: Hypothesis

A hypothesis is a proposed explanation for an observed fact, put forward so that it can be tested. It is not a random guess. "The plant died because the water was too salty" is a hypothesis only if you can go on to test it. "The plant died because it was unhappy" is not, because nothing you could observe would settle the matter.

Four conditions decide whether a hypothesis is a good one, and exam questions often ask you to name and explain them:

• Testability: it must be possible to deduce observable consequences that could confirm or refute it.
• Relevance: it must actually bear on the fact being explained, not on something unrelated.
• Simplicity: between two hypotheses explaining the same fact equally well, the simpler one is preferred.
• Fruitfulness: a good hypothesis suggests further questions and further investigations.

The hypothetical method has four steps. First, formulate the hypothesis in clear terms. Second, deduce its consequences: work out what should be observed if it were true. Third, test those consequences against evidence or experiment. Fourth, accept, revise or reject the hypothesis in the light of the test.

Verification and falsification are not the same thing. Verification is confirming a hypothesis by showing that its predicted consequences do occur. Falsification is refuting it by showing that a predicted consequence does not occur. A single failed prediction can falsify a hypothesis, whereas repeated confirmations only strengthen it without proving it beyond doubt.

A typical exam question gives you a short case, such as a doctor noticing that patients on a certain diet recover faster, and asks you to identify the hypothesis and state which condition of a good hypothesis it satisfies. Marks are usually split between stating the hypothesis in one sentence and justifying the condition you name. For worked examples, see the Class 12 Logic textbook chapter-wise solutions.

The common mistake is writing that a hypothesis is "just a guess". The fix: always add the word testable. A hypothesis is a testable explanation, and your answer should say what observation would count for or against it.

Paper Pattern and Question Types

The Logic paper is a written theory paper of 3 hours carrying 80 marks, with the remaining 20 marks coming from internal assessment. [verify] The question paper is set so that a student who has only read the chapters but never written a proof will lose marks, because part of the paper tests skills, not memory.

Questions usually fall into three weight bands. [verify]

Expect at least one question that asks you to construct a truth table for a compound proposition or to complete a formal proof from given premises. These are not questions you can answer by recalling a paragraph. For a 4-mark truth table question, the marks are normally split between the columns for each sub-formula, the final column, and the one-line conclusion about validity. If you leave out the conclusion, you lose that mark even when the table is correct.

Some sections carry internal choice, for example "Attempt any four of the following". Read the instruction line before you start writing, because students often answer more questions than required and waste time that a proof question needed. [verify]

Use the pattern to plan your revision. Chapters 1, 2 and 3 (Decision Procedure, Deductive Proof, Predicate Logic) need written practice, since the marks come from doing, not describing. Chapters 4 and 5 need both definitions and solved syllogisms. Chapters 6 and 7 are mostly conceptual, so a clear explanation with one worked example is enough. Solve at least two previous papers under timed conditions; the Class 12 Logic previous year question papers with solutions show exactly how the marks are split.

A common mistake is writing a long paragraph where a truth table was asked for. The fix: look at the verb in the question. "Construct", "prove" and "test" mean show the working; "explain" and "distinguish" mean write sentences.

Theory, Practical and Internal Assessment

Logic has no laboratory work. There is no journal to maintain and no experiment to perform. The assessment is split into two parts: a written theory paper and an internal component that your school conducts and marks. For Arts subjects under the state board pattern, this internal part is usually 20 marks out of a total of 100. [verify] Your final mark sheet therefore combines a board-conducted paper with a school-conducted assessment.

The internal component can take one of two forms, or both together. [verify] A common choice is a project file. A second possibility is an oral exam, where the teacher asks you to define terms, name rules, or explain a method aloud. Ask your Logic teacher at the start of the year which form your school follows, because the preparation is different. A project needs weeks of writing and neat presentation; an oral exam needs spoken recall of definitions and rules.

If you are given a project, pick a topic that lets you apply the syllabus rather than describe it. Two examples that work well:

• Fallacies in everyday advertisements. Collect six to eight print or screen advertisements and name the fallacy in each, with a line of reasoning. For instance, an ad that says "doctors recommend this brand" without naming the survey may be an appeal to authority.
• A set of solved proofs and truth tables. Take ten arguments from your textbook, complete the formal proof or truth table for each, and add a one-line note on whether the form is valid. This doubles as revision.

Keep the file neat and write it in your own words. Copied project material is easy for a teacher to spot and can cost you marks, and it teaches you nothing for the theory paper. Do not let the project eat the time you need for written practice: the 80-mark theory paper is still the main component, and the truth table and proof questions in it are answered only by students who have practised on paper.

What Changed in the 2020 Syllabus

The 2020 syllabus is the edition that was in force for the academic year 2019-20 and for the board exam held in 2020. If you are preparing for that exam, or you have been handed the 2020 textbook, this is the document that defines what you must study. Treat it as the final word for that year, not as a general guide to Logic.

Do not assume the 2020 list matches the current textbook. The state board revises syllabi from time to time, and later editions may have reduced, merged or reordered some topics. [verify] A chapter that appears in your 2020 syllabus may have been trimmed in a later print, and a topic added later will not appear in the 2020 list at all. Before you rely on either document, check which edition your school actually issued.

If you are using an older textbook alongside the 2020 syllabus, do one simple check. Open the contents page of the book and compare it, unit by unit, with the seven units named in the syllabus. Mark any chapter or sub-topic that appears in one but not the other. [verify] This takes ten minutes and saves you from studying a deleted topic or, worse, skipping a topic that is still examinable.

For the 2020 exam, the full syllabus was examinable unless the board issued a specific circular reducing topics. [verify] Reduction circulars are usually published separately and are not printed inside the syllabus PDF, so a syllabus copy alone will not tell you about them.

Always cross-check with your teacher before leaving out any topic. Teachers receive the circulars directly and know which sub-topics were dropped for your batch. If your teacher confirms a topic is out of scope, write "not examinable" against it in your checklist and move on. If you cannot confirm, study it. A few extra hours on a topic is a smaller cost than losing marks on a question you chose to ignore.

How to Download the Official 2020 Logic Syllabus PDF

The syllabus PDF is hosted on the state board's official website. Open the site and look for the section labelled "Syllabus", "Curriculum" or "Courses of Study". These sections are usually listed in the main menu or under a "Students" tab.

Once you are inside the syllabus section, narrow the list down step by step:

1. Select Class 12 (sometimes written as HSC or XII).
2. Select the Arts stream.
3. Select Logic from the subject list.
4. Choose the 2020 edition and your medium (English or Marathi).

The file will open as a PDF in your browser. Save it to your phone or computer instead of only reading it online. A saved copy lets you check a sub-topic in the middle of revision without hunting for the link again, and it works when your data pack runs out.

If the official site no longer hosts the 2020 edition, the board may have replaced it with a newer one. [verify] In that case, ask your school library or your Logic teacher for a printed copy of the 2020 syllabus. Schools usually keep copies of past syllabus documents on file. [verify]

If you are collecting syllabi for other subjects too, the Class 12 syllabus hub page lists them for the 2020 academic year in one place.

How to Use the Syllabus for Exam Preparation

A syllabus becomes useful only when you convert it from a reading document into a working tool. The method below takes about one hour to set up and then saves you many hours during revision.

Step 1: Build a checklist. Open the syllabus and copy every sub-topic under the seven units into a notebook or a spreadsheet, one line each. Keep the wording close to the syllabus so you do not miss the depth it expects. For example, under Decision Procedure the syllabus may list "truth tables for two variables" and "truth tables for three variables" separately. Those are two ticks, not one. Tick a line only after you can answer a question on it without looking at the book.

Step 2: Split each chapter into memory work and skill work. Some parts of Logic must be memorised; others must be practised with a pen. Write both lists for every chapter:

• Memorise: definitions (validity, soundness, distribution of terms), the square of opposition relations, rules of inference, valid moods of the four figures, the five methods of induction.
• Practise: drawing truth tables, writing formal proofs line by line with justifications, translating sentences into quantifier notation, testing syllogisms with Venn diagrams, identifying which inductive method an example uses.

Memory work can be revised in short bursts. Skill work needs solved examples and then unsolved ones. If you only read proofs instead of writing them, you will lose marks on the construction question.

Step 3: Weight your time. Chapters that carry more marks or that you find difficult get more slots in your timetable. If Traditional Logic and Syllogism carry more questions, [verify] give them two revision slots for every one you give to a lighter chapter. Be honest about weak areas: a chapter you dislike is usually the one where you drop marks.

Step 4: Write your own question bank. For each sub-topic, frame one short-answer question (2 marks) and one long-answer question (4 to 6 marks). [verify] For instance, for "square of opposition" a short question could ask you to state the contradictory of a given proposition, and a long question could ask you to explain all four relations with examples. Solving your own questions tests understanding better than re-reading notes, and it mirrors how the paper actually asks things.

Step 5: Revise only from your checklist in the final week. By then the textbook has done its job. Go through the ticked lines, attempt the questions you framed, and revisit only the lines you cannot tick. If a line stays unticked, open the matching chapter solutions and work through solved examples before trying again.

Frequently Asked Questions

How many chapters are there in the Class 12 Logic syllabus for 2020?

The 2020 Logic course has seven units, and each unit corresponds to one chapter of your textbook. They run from Decision Procedure through Predicate Logic, Traditional Logic and Syllogism to the remaining units. Treat the unit order as a study order, because later chapters assume the tools taught earlier.

What is the marks distribution for Class 12 Logic in the state board exam?

The syllabus document does not print a fixed mark for every unit. It lists the seven units with sub-topics and learning outcomes, and the paper is set from those outcomes. Use the outcomes to judge weight: a unit with many outcomes usually carries more questions. For the exact question-wise marks split, check the board's paper pattern for your year [verify].

Is there a practical or project component in Class 12 Logic?

Logic is assessed through the written theory paper. The 2020 syllabus document sets out units, sub-topics and learning outcomes, and it does not describe a separate practical exam or project file for the subject. If your college announces an internal project or oral, follow the college's instruction, since internal assessment rules can differ by institution [verify].

Is the 2020 Logic syllabus the same as the current syllabus?

Not necessarily. The 2020 document is the edition issued for that academic year, and the board can revise units or outcomes later. Compare the unit list and outcomes in your current textbook with the 2020 version before relying on it. If the two match, your 2020-based notes remain valid; if not, study from the current edition [verify].

Is the Class 12 Logic syllabus available in Marathi medium?

Yes. The syllabus is published in both English and Marathi medium, and the units, sub-topics and learning outcomes are identical in the two versions. Only the language of the textbook and question paper changes. A Marathi-medium student therefore prepares exactly the same content as an English-medium student, so you can use either version to plan your study.

How long is the Class 12 Logic board exam paper?

The Logic paper follows the standard HSC written paper duration, which is three hours. The syllabus itself does not state the duration; it comes from the board's exam pattern for the year. Confirm the timing printed on your hall ticket, and practise full papers within that limit so your truth tables and proofs fit the time [verify].