The negation of is
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Answer: Option B —
Detailed Solution
By De Morgan's law, .
The conjunction is false exactly when at least one of , is false.
✓ Check
= T, = F: = F, and = F ∨ T = T, the opposite value.⚠ Common trap
(A) — negates each part but forgets to change ∧ to ∨.Quick tip
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Mathematical Logic — Preparation
This question tests your understanding of Mathematical Logic, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Mathematical logic deals with statements that are either true or false, and with how they combine. This topic covers statements and logical connectives (negation, conjunction "and", disjunction "or", conditional "if...then" and biconditional "if and only if"), truth tables, tautologies, contradictions and contingencies, and logical equivalence. It also covers the converse, inverse and contrapositive of a conditional statement, quantifiers ("for all" and "there exists"), the negation of compound and quantified statements, De Morgan's laws, and switching circuits. Remember that a conditional statement p -> q is false only when p is true and q is false, and that it is logically equivalent to its contrapositive ~q -> ~p. Mathematical logic is a high-scoring chapter in MHT CET because its questions follow fixed rules and can be checked with truth tables. Practise the mathematical logic questions below, each with a truth table or step-by-step solution.