JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Analyzing +4 | -1

Let

r \in \{ p,\,q,\, \sim p,\, \sim q\}

be such that the logical statement

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

is a tautology. Then

r

is equal to:

View answer and explanation

Correct option: C

\sim p

Option C (

\sim p

) is correct because it makes the logical statement a tautology, meaning it is always true regardless of the truth values of p and q.

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{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)

p

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p \Leftrightarrow q