Question

Consider the experiment of rolling a die. Let $A$ be the event of 'getting a prime number' and $B$ be the event of 'getting an odd number'. Then which of the following is/are true?

• A. The set $A\text{or}B=\{1,2,3,5\}$
• B. The set $A\text{and}B=\{3,5\}$
• C. The set $A\text{but not}B=\left\{2\right\}$
• D. The set $A\text{and}B=\{1,2,3,5\}$

Answer 1

Answer: (A), (B), (C)

The set $A\text{but not}B=\left\{2\right\}$

We have, $S=\{1,2,3,4,5,6\}$
$A=\{2,3,5\}$ and $B=\{1,3,5\}$
Clearly we have,
$A\text{or}B=A\cup B=\{1,2,3,5\}$
Similarly, we have $A\text{and}B=A\cap B=\{3,5\}$
$A\text{but not}B=A-B=\left\{2\right\}$