Prove by direct method that for any real number $x, y$ if $x=y$, then $x^2=y^2$.
Let $p: x=y, \quad x, y \in R$
On squaring both sides,
$$\begin{gathered} x^2=y^2: q \quad\text{[say]}\\ p \Rightarrow q \end{gathered}$$
Hence, we have the result.
Using contrapositive method prove that, if $n^2$ is an even integer, then $n$ is also an even integer.
Let $p: n^2$ is an even integer.
$q: n$ is also an even integer.
Let $\sim p$ is true i.e., $n$ is not an even integer.
$\Rightarrow n^2$ is not an even integer. $\quad$ [since, square of an odd integer is odd]
$\Rightarrow \sim p$ is true.
Therefore, $\sim q$ is true $\Rightarrow \sim p$ is true.
Hence proved.
Which of the following is a statement?
Which of the following is not a statement.
The connective in the statement ' $2+7>9$ or $2+7<9$ ' is