If p and q are logical statements, then ~ p → p → q is equivalent to

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Question: Answered & Verified by Expert

If

p

and

q

are logical statements, then

(~ p) \to (p \to q)

is equivalent to

MathematicsMathematical ReasoningJEE Main

Options:

A $p \land q$
B $p \to (p \lor q)$
C $p \lor q$
D $(p \lor q) \leftrightarrow (p \land q)$

Solution:

2422 Upvotes Verified Answer

The correct answer is:

p \to (p \lor q)

∴ s \to t \equiv \sim s \lor t

∴ (~ p) \to (p \to q) \equiv (p) \lor (p \to q)

\equiv (p) \lor (\sim p \lor q)

\equiv (p \lor \sim p) \lor q

\equiv t \lor q \equiv t

Also,

p \to (p \lor q) \equiv \sim p \lor (p \lor q) \equiv t

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