Question

Consider the experiment of rolling a die. Let $A$ be the event ‘getting a prime number’, $B$ be the event ‘getting an odd number’. Write the set representing the events
$\left(i\right)$ $A\text{or}B$.
$\left(ii\right)$ $A\text{and}B$.
$\left(iii\right)$ $A\text{but not}B$.
$\left(iv\right)$ ${}^{\prime }\text{not}{A}^{\prime }$.

Answer 1

If a dice is rolled then the possible outcomes are $(1,2,3,4,5,6)$
$\Rightarrow S=\{1,2,3,4,5,6\}$
$A$ be the event of ‘getting a prime number’
$B$ be the event of ‘getting an odd number’.
So,
$A=\{2,3,5\},B=\{1,3,5\}$
$\left(i\right)$ $A\text{or}B=A\cup B=\{1,2,3,5\}$.
$\left(ii\right)$ $A\text{and}B=A\cap B=\{3,5\}$.
$\left(iii\right)$ $A\text{but not}B=A-B=\left\{2\right\}$.
$\left(iv\right)$ ${}^{\prime }\text{not}{A}^{\prime }=A^{\prime }=S-A=\{1,4,6\}$.