JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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The conditional statement

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

is:

View answer and explanation

Correct option: A

A tautology

Option A (A tautology) is correct because the given statement is of the form (A -> B) v (B -> A), which is always true regardless of the truth values of A and B.

More Questions from MATHEMATICAL REASONING

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p:A

man is happy

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

and

q

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

p \rightarrow q

is Let

{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

{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

is odd and

q:

Natural number

n

is not divisible by 2 , then the biconditional statement

p \Leftrightarrow q