Set $U = {1, 2, 3, 4, 5, 6, 7, 8, 9}$ , $A = {x : x \in N, 30 \leq x^{2} \leq 70}$ , $B = {x : x$ is a prime number $< 10}$ . Which of the following does NOT belong to the set ${(A - B)}^{'}$ ?

4

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5

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6

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9

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Solution

The correct option is B $6$
Given, $U = {1, 2, 3, 4, 5, 6, 7, 8, 9}$
$A = {x : x \in N, 30 \leq x^{2} \leq 70}$
So, $A = {6, 7, 8}$ and $A^{'} = {1, 2, 3, 4, 5, 9}$
$B = {x : x is a prime number < 10}$
So, $B = {2, 3, 5, 7}$ and $B^{'} = {1, 4, 6, 8, 9}$
$\Rightarrow A \cap B = {7}$
$(A - B)^{'} = U - (A - B)$
$= U - [A - (A \cap B)]$
$= {1, 2, 3, 4, 5, 6, 7, 8, 9} - [{6, 7, 8} - {7}]$
$= {1, 2, 3, 4, 5, 6, 7, 8, 9} - [{6, 8}]$
$= {1, 2, 3, 4, 5, 7, 9}$
So, $6$ and $8$ does not belong to $(A - B)^{'}$ .

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Set U={1,2,3,4,5,6,7,8,9}, A={x:x∈N,30≤x2≤70}, B={x:x is a prime number <10}. Which of the following does NOT belong to the set (A−B)′ ?

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