Let p , q and r be three statements, then ~ p → q → r is equivalent to

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Question: Answered & Verified by Expert

Let

p, q

and

r

be three statements, then

(~ p \to q) \to r

is equivalent to

MathematicsMathematical ReasoningJEE Main

Options:

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

Solution:

1462 Upvotes Verified Answer

The correct answer is:

(p \to r) \land (q \to r)

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

\equiv ~ (p \lor q) \lor r

\equiv (~ p \land ~ q) \lor r

\equiv (~ p \lor r) \land (~ q \lor r) \equiv (p \to r) \land (q \to r)

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