The contrapositive of the statement p (q r) is

Correct Answer is : (r∨∼q)→∼p({r} {q}) arrow {p}(r∨∼q)→∼p

Correct Answer is : (r∨∼q)→∼p({r} {q}) arrow {p}(r∨∼q)→∼p

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MHTCET 23 Apr 2025 Shift 1 Paper

Question : 137 of 150

Marks: +1, -0

\sim p \vee(q \wedge \sim r)

Solution:

Concept:

The contrapositive of an implication

p \rightarrow q

\sim q \rightarrow \sim p

Explanation:

First, rewrite the given statement using the conditional law.

\sim p \vee (q \wedge \sim r) \equiv p \rightarrow (q \wedge \sim r)

Now, apply the contrapositive rule to

p \rightarrow (q \wedge \sim r)

It becomes

\sim (q \wedge \sim r) \rightarrow \sim p

Use De Morgan's law on the left side:

\sim (q \wedge \sim r) \equiv \sim q \vee r

So we get

(\sim q \vee r) \rightarrow \sim p

By the commutative law,

\sim q \vee r \equiv r \vee \sim q

Therefore, the contrapositive is

(r \vee \sim q) \rightarrow \sim p

Answer:

(r \vee \sim q) \rightarrow \sim p

Which matches option D.

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