The negation of (p q) arrow((p r) arrow q) is equivalent to ...

Correct Answer is : p∧qp qp∧q

Correct Answer is : p∧qp qp∧q

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MHTCET 17 Apr 2026 Shift 2 Paper

Question : 109 of 150

Marks: +1, -0

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

is equivalent to ...

Solution:

Concept:

Use the negation of an implication:

\neg (A \rightarrow B) \equiv A \wedge \neg B

Explanation:

Given statement:

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

Negate it using

\neg (A \rightarrow B) \equiv A \wedge \neg B

So, negation =

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

Again apply the same rule inside:

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

Since

\sim(\sim q) \equiv q

, we get

(p \vee r) \wedge q

Therefore, the full negation becomes

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

Because

(p \wedge q)

is true, it forces

p

to be true, making

(p \vee r)

already true.

Also

q

is already included in

p \wedge q

Thus the expression simplifies to

p \wedge q

Answer:

Option A:

p \wedge q

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