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.

Explanation

Let P: The interger n is odd.
And `q:n^2 `is odd.

First n be odd: Then,
`n=(2k+1)` for some interger K.

Then `n^2(2k+1)^2=(4k^2+4k+1)=2(2k^2+2k)+1 `

This n^2 is 1 more than an even number and therefore ,it is odd.

Thus `p⇒q`

Now ,in order to prove that `q⇒p` it is sufficient to show
that `~p⇒q`[Contrapositive method ]

Clearly `~ P` The interge n is even

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