Question

Using the words “necessary and sufficient” rewrite the statement “The
integer
n
is odd if and only if
n
2
is odd”. Also check whether the statement is true.

Answer 1

P is sufficient for Q
\[\Large P \rightarrow Q\]

P is necessary for Q
\[\Large Q \rightarrow P\]

P is sufficient and necessary for Q
\[\Large P \iff Q\]

Answer 2

or necessary and sufficient... same thing, basically :D

Answer 3

Thankyou sir

Answer 4

:)

Answer 5

As for proving its truth, it is enough to show that if an integer n is odd, then \(n^2\) is odd
and if an integer n is even, then \(n^2\) is even.