Verify: $x\times(y\times z)=(x\times y)\times z$, where $x=\frac{1}{2},\ y=\frac{1}{3}$ and $z=\frac{1}{4}$.
Given: $x=\frac{1}{2},\ y=\frac{1}{3}$ and $z=\frac{1}{4}$.
To do: To verify: $x\times(y\times z)=(x\times y)\times z$.
Solution:
$L.H.S.=x\times( y\times z)$
$=\frac{1}{2}\times ( \frac{1}{3}\times \frac{1}{4})$
$=\frac{1}{2}\times ( \frac{1}{12})$
$=\frac{1}{24}$
Now, $R.H.S.=(x\times y)\times z$
$=(\frac{1}{2}\times\frac{1}{3})\times \frac{1}{4}$
$=( \frac{1}{6})\times \frac{1}{4}$
$=\frac{1}{24}$
Thus, $L.H.S.=R.H.S.$
hence verified.
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