Question

Verify the property $x+y=y+x$ of rational numbers by using $x=\frac{1}{2}$and $y=\frac{1}{2}$.

Answer 1

Verifying the property $x+y=y+x$ for given $x$ and $y$:

Taking L.H.S.,

$\begin{array}{rcl}x+y& =& \frac{1}{2}+\frac{1}{2}\\ & =& \frac{1+1}{2}\\ & =& \frac{2}{2}\\ & =& 1\end{array}$

Taking R.H.S.,

$\begin{array}{rcl}y+x& =& \frac{1}{2}+\frac{1}{2}\\ & =& \frac{1+1}{2}\\ & =& \frac{2}{2}\\ & =& 1\end{array}$.

On comparing both L.HS. and R.H.S., we get,

$L.H.S=R.H.S.=1$

Hence, the property $x+y=y+x$ is verified.