The inverse of p arrow(q arrow r) is logically equivalent to

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

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

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MHTCET 10 May 2024 Shift 1 Paper

Question : 146 of 150

Marks: +1, -0

The inverse of

p \rightarrow(q \rightarrow r)

is logically equivalent to

Solution:

Concept:

For an implication

A \rightarrow B

, the inverse is

\sim A \rightarrow \sim B

Explanation:

Let

A = p

and

B = (q \rightarrow r)

So the inverse of

p \rightarrow (q \rightarrow r)

is:

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

Now, the contrapositive of

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

(q \rightarrow r) \rightarrow p

Therefore, the inverse is logically equivalent to

(q \rightarrow r) \rightarrow p

Answer:

Option D:

(q \rightarrow r) \rightarrow p

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