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

Step-by-step 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