The contrapositive of the statement pattern [p (p arrow q)] arrow(p q) is

Correct Answer is : (∼p∨q)→[∼p∧(p∧∼q)]( p q) arrow[ p (p q)](∼p∨q)→[∼p∧(p∧∼q)]

Correct Answer is : (∼p∨q)→[∼p∧(p∧∼q)]( p q) arrow[ p (p q)](∼p∨q)→[∼p∧(p∧∼q)]

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MHTCET 18 Apr 2026 Shift 1 Paper

Question : 111 of 150

Marks: +1, -0

[p \vee(p \rightarrow q)] \rightarrow(p \wedge \sim q)

Solution:

Concept:

The contrapositive of

A \rightarrow B

\sim B \rightarrow \sim A

Explanation:

Given statement pattern:

[p \vee(p \rightarrow q)] \rightarrow(p \wedge \sim q)

Let

A = p \vee(p \rightarrow q)

and

B = p \wedge \sim q

First, find

\sim B

using De Morgan's law:

\sim B = \sim(p \wedge \sim q) = \sim p \vee q

Now find

\sim A

\sim A = \sim[p \vee(p \rightarrow q)] = \sim p \wedge \sim(p \rightarrow q)

Using the equivalence

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

, we get:

\sim A = \sim p \wedge(p \wedge \sim q)

Thus, the contrapositive is:

(\sim p \vee q) \rightarrow[\sim p \wedge(p \wedge \sim q)]

This matches Option D.

Answer:

Option D:

(\sim p \vee q) \rightarrow[\sim p \wedge(p \wedge \sim q)]

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