Question

If A and B are two sets such that n(A)=23,n(B)=22 and n(A∩B)=15,n(U)=60, where U is a universal set. Then n(neither A nor B) is:​

Answer 1

Answer:

ABC

Step-by-step explanation:

I Don't Know A or B

Answer 2

SOLUTION

GIVEN

A and B are two sets such that n(A) = 23 , n(B) = 22 and n(A∩B) = 15 , n(U) = 60, where U is a universal set

TO DETERMINE

n(neither A nor B)

EVALUATION

Here it is given that A and B are two sets such that n(A) = 23 , n(B) = 22 and n(A∩B) = 15 , n(U) = 60, where U is a universal set

Thus we get

n(A ∪ B)

= n(A) + n(B) - n(A∩B)

= 23 + 22 - 15

= 30

Now n(neither A nor B)

$\sf{ = n(A' \cap \: B')}$

$\sf{ = n((A\cup \: B)')}$

$\sf{ = n(U) - n(A\cup \: B)}$

$\sf{ = 60 - 30}$

$\sf{ = 30}$

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