# If n(U) = 20, n(A)=12, n(B)=9,$n\left ( A\cap B \right )= 4$ where U is the universal set, then $n\left ( A\cup B \right )^{c}=$ Option 1) 17 Option 2) 9 Option 3) 11 Option 4) 3

H Himanshu

As we learnt

UNION OF SETS -

Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union.

- wherein

Symbolically, we write A U B = {x: x ∈ A or x ∈ B}.

n(A U B) = n(A) + n(B) - n(A$\cap$B)

=12+9-4=17

n(A U B)'=20-17=3

Option 1)

17

Option 2)

9

Option 3)

11

Option 4)

3

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