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JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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The statement ∼[p∨(∼(p∧q))]\sim[p \vee(\sim(p \wedge q))] is equivalent to
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Correct option: D
∼(p∨q)\sim(p \vee q)
Option D (∼(p∨q)\sim(p \vee q)) is correct because by applying De Morgan's laws and simplification rules, the given statement is logically equivalent to ∼p∧∼q\sim p \wedge \sim q, which is the same as ∼(p∨q)\sim(p \vee q).

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If p:Ap:A man is happy
q:Aq:A man is rich
Then, the statement, "If a man is not happy, then he is not rich" is written as Consider the following compound statements.
(i) Mumbai is the capital of Rajasthan or Maharashtra.
(ii) 3\sqrt{3} is a rational or an irrational number.
(iii) 125 is a multiple of 7 or 8 .
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true? Let pp and qq be two Statements. Amongst the following, the Statement that is equivalent to p→qp \rightarrow q is Let F1(A, B, C)=(A∧∼B)∨[∼C∧(A∨B)]∨∼A{F_1}(A,\,B,\,C) = \left( {A \wedge \sim B} \right) \vee \left[ { \sim C \wedge \left( {A \vee B} \right)} \right] \vee \sim A and F2(A, B)=(A∨B)∨(B→ ∼ A){F_2}(A,\,B) = \left( {A \vee B} \right) \vee (B \to \, \sim \,A) be two logical expressions. Then, The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is : Suppose pp : A natural number nn is odd and q:q: Natural number nn is not divisible by 2 , then the biconditional statement p⇔qp \Leftrightarrow q is
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