(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.
