Question

Let $A=\{x:x\text{is a prime factor of}240\}$ and $B=\{y:y\text{is the sum of any two prime factors of}240\}$. Then which of the following options is true?

• A. $5\notin A\cap B$
• B. $7\in A\cap B$
• C. $8\in A\cap B$
• D. $8\in A\cup B$

Answer 1

The correct option is D $8\in A\cup B$

$A=\{x:x\text{is a prime factor of}240\}$
$240=2^4\times 3\times 5$
$\therefore A=\{2,3,5\}$

$B=\{y:y\text{is the sum of any two prime factors of}240\}$
$\therefore B=\{5,7,8\}$
$\Rightarrow A\cup B=\{2,3,5,7,8\}$
and $A\cap B=\left\{5\right\}$