Rewrite the following statements with ‘if-then’ in five different

1.	Rewrite the following statements with ‘if-then’ in five different ways conveying the same meaning. (i) ‘If a natural number is odd, then its square is also odd’
Answer» (i) Given: ‘If a natural number is odd, then its square is also odd. Let p : a natural number is odd q : a natural number square is also odd. Then, if p then q is same as p ⇒q (p implies q) i.e., A natural number is odd implies that its square is also odd. p is sufficient condition for q e., for the square of a natural number to be odd it is sufficient that the number itself is odd. p only if q e., A natural number is odd only if its square is odd. q is a necessary condition for p e., for a natural number to be odd it is necessary that its square must be odd. ~q implies ~p If the square of a natural number is not odd, then the number itself is also not odd.

Rewrite the following statements with ‘if-then’ in five different ways conveying the same meaning. (i) ‘If a natural number is odd, then its square is also odd’

Answer»

(i) Given: ‘If a natural number is odd, then its square is also odd.

Let p : a natural number is odd

q : a natural number square is also odd. Then, if p then q is same as

p ⇒q (p implies q)
i.e., A natural number is odd implies that its square is also odd.
p is sufficient condition for q e., for the square of a natural number to be odd it is sufficient that the number itself is odd.
p only if q e., A natural number is odd only if its square is odd.
q is a necessary condition for p e., for a natural number to be odd it is necessary that its square must be odd.
~q implies ~p
If the square of a natural number is not odd, then the number itself is also not odd.