The logical equivalence of the given expression P→ (q → r) will be (p ∧ q) → r. Both these expressions result in the same outcome.
Here, we are given an expression, that is, P→(q→r). We need to find it's logical equivalence.
A statement is a logical equivalence of another if and only if they have the same resulting truths.
We have,
P → (q → r)
= P → (∼q → r)
= p → (∼q ∨ r)
= ∼p ∨ (∼q ∨ r)
= (∼p ∨ ∼q) ∨ r
= ∼ (p ∧ q) ∨ r
= (p ∧ q) → r
Hence, we find that the logical equivalence of the expression, P→ (q → r) is (p ∧ q) → r.
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