The contrapositive of the inverse of {p} arrow({p} arrow {q}) is

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

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

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MHTCET 15 May 2024 Shift 2 Paper

Question : 107 of 150

Marks: +1, -0

\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})

Solution:

Concept:

The inverse negates both parts; the contrapositive swaps and negates both parts.

Explanation:

For

p \rightarrow (p \rightarrow q)

, the inverse is:

\sim p \rightarrow \sim(p \rightarrow q)

Now take the contrapositive of this inverse:

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

This simplifies to:

(p \rightarrow q) \rightarrow p

Since

p \rightarrow q \equiv \sim p \vee q

, we get:

(\sim p \vee q) \rightarrow p

Answer:

Option B:

(\sim p \vee q) \rightarrow p

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