Question

Use known logical equivalences to prove that a → (b → c) is logically equivalent to (a ^ b) → c.

Answer 1

Answer:-

a ∨ ( b ∨ c ) ⇔ (a ∨ b )∨ c ⇔ (a∧b)∨c ⇔(a∧b)→c

Explanation:

Explanation :-

we know that b→ c ⇔ b∨c

Replacing b→ c ⇔ b ∨ c , we get

a → b ∨ c ,

By the same rule b→ c ⇔ b∨c

⇒ a ∨ ( b ∨ c )

Now

a ∨ ( b ∨ c ) ⇔ (a ∨ b )∨ c ⇔ (a∧b)∨c ⇔(a∧b)→c