Question

Rewrite the following statement, with 'if ..., then' in five different ways conveying the same meaning :

If a natural number is even, then its square is even.

Answer 1

We may rewrite it in following ways:

(i) A natural number is even, implies that, its square is even.

(ii) A natural number is even only if its square is even.

(iii) For a natural number to be even it is necessary that its square is even.

(iv) For the square of a natural number to be even, it is sufficient that the number is even.

(v) If the square of a natural number is not even, then the natural number is not even.