Solution:
(i) The given statement is compound statement then components are,
$P$: $\mid{x}\mid$ is equal to $x$.
$\sim p$: $\mid{x}\mid$ is not equal to $x$.
$q$: $\mid{x}\mid$ is equal to $–x$.
$\sim q$: $\mid{x}\mid$ is not equal to $-x$.
$\left( p\vee q \right)=$ $\mid{x}\mid$ is equal to either x or $– x$.
$\sim \left( p\vee q \right)=\sim p\wedge \sim q=$ $\mid{x}\mid$ is not equal to $x$ and $\mid{x}\mid$ is not equal to $– x$.
Solution:
(ii) The statement given is compound statement whose components are,
$P$: 6 is divisible by 2
$\sim p$: 6 is not divisible by 2
$q$: 6 is divisible by 3
$\sim q$: 6 is not divisible by 3.
$\left( p\vee q \right)=$ 6 is divisible by 2 and 3.
$\sim\left( p\wedge q \right)=\sim p\vee \sim q=$ 6 is neither divisible by 2 nor 3