Question

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

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

• 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 in which the elements common in both A and B are present.

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

$\therefore$ $A\cap B$ = {2, 3, 5, 7}