JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Analyzing +4 | -1

Consider the following two propositions:

P1:\,\, \sim (p \to \sim q)\,

P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)

If the proposition

p \to (( \sim p) \vee q)

is evaluated as FALSE, then:

View answer and explanation

Correct option: C

Both P1 and P2 are FALSE

Option C (Both P1 and P2 are FALSE) is correct because when

p \to (\sim p \vee q)

is FALSE, it implies

p

is TRUE and

q

is FALSE, making both P1 and P2 FALSE.

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p:A

q:A

\sqrt{3}

p

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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)

p

n

q:

n

p \Leftrightarrow q