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JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Application +4 | -1

Simplify

\left( {p \vee q} \right) \wedge \left( {p \vee \sim q} \right)

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Correct option: A

p

Option A (

p

) is correct because the expression simplifies to

p

using the distributive and complement laws of Boolean algebra.

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p:A

q: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)

\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

p

q

be two Statements. Amongst the following, the Statement that is equivalent to

p \rightarrow q

{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

{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

p

: A natural number

n

q:

n

is not divisible by 2 , then the biconditional statement

p \Leftrightarrow q