Solution:

(i) The sentence given is a compound statement whose components are

$p$: $x = 2$ is a root of the Quadratic equation $x^{2}{-}5x + 6 = 0$.

$\sim p$: $x = 2$ is not a root of the Quadratic equation $x^{2}{-}5x + 6 = 0$.

$q$: $x = 3$ is a root of the Quadratic equation $x^{2}{-}5x + 6 = 0$.

$\sim q$: $x = 3$ is not a root of the Quadratic equation $x^{2}{-}5x + 6 = 0$.

$\left( p\wedge q \right)=x=2$ and $x = 3$ are roots of the Quadratic equation $x^{2}{-}5x + 6 = 0$.

$\sim \left( p\wedge q \right)=\sim p\vee \sim q=$ Neither $x = 2$ and nor $x = 3$ are roots of $x^{2}{-}5x + 6 = 0$

Solution:

(ii) The statement given is compound statement whose components are,

$P$: A triangle has three sides

$\sim p$: A triangle doesn’t have three sides.

$q$: A triangle has four sides.

$\sim q$: A triangle doesn’t have four side.

$\left( p\vee q \right)=$ A triangle has either three-sides or four-sides.

$\sim \left( p\vee q \right)=\sim p\wedge \sim q=$ A triangle has neither three sides nor four sides.