Playbook
Mathematical Logic
84 q - 1.96/paper - 29% HARD. The one chapter in MHT-CET Maths with its own execution mode: 70% of its stems ask which statement is true, against roughly 0% everywhere else. Its 31% HARD overstates the cost, because the difficulty is front-loaded into learning ONE technique (build the truth table) that then applies to every question - and it is not spread evenly: Switching Circuits is 10 q at 60% HARD while Negation is 14 q at 14%.
- Questions in the bank
- 84
- q/paper (2024–25 shifts)
- 1.96
- Tagged HARD
- 29%
- Subtopics
- 6
Strand: Quick-Win
When you’ll see it
Statements, connectives and quantifiers — or a switch circuit diagram, which is the same thing drawn differently.
How this chapter is tested
84 q at 1.96 per paper and 29% HARD. This is the one chapter in MHT-CET Maths with its own execution mode: around 70% of its stems ask which of the four statements is true, against roughly 0% everywhere else in the subject. Every other chapter hands you a problem to solve; this one hands you four claims to adjudicate. That difference is worth more than any formula on this page, because it changes what you do when you read the question.
The 31% HARD figure overstates the cost, and it is worth understanding why. The difficulty here is front-loaded into TWO techniques that answer between them almost every question in the chapter: build the truth table, and simplify with the algebra of statements. The table always terminates but is slow; the algebra is fast but needs the ten laws at your fingertips. Learn the table first and the algebra second — and note that the fast route is the one the harder subtopics assume. Once both are automatic, a HARD logic question and a MODERATE one take about the same amount of time. Compare that with Indefinite Integration, where every new integrand is a fresh recognition problem.
Switching Circuits is the chapter's smallest subtopic and by a wide margin its hardest — 10 q at 60% HARD, against 14% for Negation — and it intimidates students who have not been told the translation. It is two rules: switches in series are AND, switches in parallel are OR. After that a circuit is a logical expression and the same truth table answers it, which is why a subtopic that looks like the chapter's wall is actually its cheapest block of marks per hour spent.
The tactic follows from the execution mode. With four claims and no negative marking, building the truth table and evaluating all four options is a complete method that always terminates — and a partially built table plus elimination still beats leaving the question blank, because a blank and a wrong answer cost the same nothing.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Statements, connectives and truth tables
Construct the table for any compound statement and read the truth value off it. 12 q at 33% HARD, and the technique that every other skill in this chapter runs on. Learn it first and learn it properly.
Finding truth values of component statements
The chapter's signature move, run backwards: you are told the pattern is FALSE and asked for p, q and r. 15 q at 20% HARD. A conditional is false in exactly one row, which forces the values rather than leaving you to search.
Negation of statements and quantifiers
Negate compound statements, conditionals, biconditionals and quantified statements. 14 q at 14% HARD — the cheapest block in the chapter, which is precisely why a mechanical slip here is so expensive.
Converse, inverse, and contrapositive
Given a conditional, write its three relatives and know that only the contrapositive is logically equivalent to it. 17 q at 24% HARD — the chapter's largest block and pure pattern work.
Logical equivalence and algebra of statements
Test two expressions for equivalence, simplify with the distributive and absorption laws, and classify a pattern as a tautology, contradiction or contingency from its final column. 16 q at 31% HARD.
Switching circuits
Translate a circuit into a logical expression — series is AND, parallel is OR — then simplify or test it exactly as you would any other statement. 10 q at 60% HARD, the densest HARD block here, and much cheaper than it looks once the translation is automatic.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Negation of a conditional written as another conditional
Denying an implication asserts the antecedent and denies the consequent; it is not another implication. The tempting wrong option negates both parts and keeps the arrow.
Converse offered where the contrapositive is asked
Only the contrapositive shares the truth value of the original. Converse and inverse are equivalent to each other and to neither, and all three appear in the option list.
Quantifier negated without negating the predicate
Negating a for-all statement gives a there-exists statement whose inner claim is ALSO negated. Options that flip only the quantifier are the standard distractor.
Parallel branch read as an AND
In a switch circuit, current flows if EITHER parallel branch is closed. Reading parallel as AND inverts the expression and produces a clean but wrong simplification.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Mathematical Logic notesDrill every mathematical logic question
84 questions from the bank, scoped to 6 bundled subtopics.
Drill one subtopic at a time
The 6 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.