Write the converse, inverse, contrapositive of the following statement. If a man is bachelor, then he is happy.

QUESTION

Miscellaneous Exercise 1 | Q 4.15 | Page 33

Write the converse, inverse, contrapositive of the following statement.

If a man is bachelor, then he is happy.

SOLUTION

Let p : A man is bachelor.
q : A man is happy.

∴ The given statement is p → q.

Its converse is q → p.
If a man is happy then he is bachelor.

Its inverse is ~p → ~q.
If a man is not bachelor then he is not happy.

Its contrapositive is ~q → ~p.
If a man is not happy then he is not bachelor.