Question

The statement "If a natural number is odd, then its square is also odd" can be written with 'if- then' in following different ways.
(i) A natural number is odd implies that its square is odd.
(ii) A natural number is odd only, if its square is odd.
(iii) If the square of a natural number is not odd, then the natural number is also not odd.
(iv) For a natural number to be odd, it is necessary that its square is odd.
(v) For a square of a natural number to be odd, it is sufficient that the number is odd.
Then, which of the following is/are true from of the given statements?

• A. (i) and (ii)
• B. (iii) and (iv)
• C. Only (v)
• D. All are true

Answer 1

Answer: (D)

Given statement can be written in the following ways.
(i) A natural number is odd implies that its square is odd.
(ii) A natural number is odd only, if its square is odd.
(iii) If the square of a natural number is not odd, then the natural number is also not odd.
(iv) For a natural number to be odd, it is necessary that its square is odd.
(v) For a square of a natural number to be odd, if it is sufficient that the number is odd.