The statement $(p \to (q \to p)) \to (p \to (p \vee q))$ is

Equivalent to $(p \wedge q) \vee ( \sim q)$

Equivalent to $(p \vee q) \wedge ( \sim p)$

JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Analyzing +4 | -1

The statement

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

View answer and explanation

Correct option: D

a tautology

Option D is correct because the truth table of the given statement results in all true values, indicating it is a tautology.

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p:A

q:A

\sqrt{3}

p

q

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