Question

If $A=\{x:x\text{is a prime number}\}$ and

$B=\{x:x\le 10,x\in N\},$ then $A\cap B$ = ___.

• A. $\{1,3,5,7\}$
• B. $\{3,5,7\}$
• C. $\{2,3,5,7\}$
• D. $\{1,2,3,5,7\}$

Answer 1

The correct option is C $\{2,3,5,7\}$

$A=\{x:x\text{is a prime number}\}$
$\Rightarrow A=\{2,3,5,7,11,13,17,...\}$

$B=\{x:x\le 10,x\in N\}$
$\Rightarrow B=\{1,2,3,4,5,6,7,8,9,10\}$

$A\cap B$ is defined as the set of elements common to both A and B.

$\Rightarrow A\cap B=\{2,3,5,7,11,13,17,...\}\cap \{1,2,3,4,5,6,7,8,9,10\}$
$=\{2,3,5,7\}$