Question

Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 

Answer 1

If a man is a bachelor , then he is unhappy.

Let P : A man is a bachelor
      q : He is unhappy
(a) Its converse is q → p
i.e. , If a man is unhappy then he is a bachelor.
(b) Its inverse is ∼ p → ∼ q
i.e. , If a man is not bachelor then he is happy.
(c) Its contrapositive is ∼ q → ∼ p
i.e., If a man is happy then he is not a bachelor.