Question

If A and B are two sets and U is the universal set such that n(A) = 100 n(B) = 200 n(U) = 500 and
n(An B) = 50, find n(A'n B').​

Answer 1

Answer:

Given :-

n (U) = 500

n (A) = 100

n(B) = 200

n (A ∩ B) = 50

Now , we know that :-

(A' ∩ B') = n (A U B)'

To find n (A U B)' we have to use the formula for n (A U B)

n (A U B) = n (A) + n (B ) - n (A ∩ B)

= 100 + 200 - 50

= 300 - 50

= 250

n (A U B)' = n (U) - n (A U B)

= 500 - 250

= 250

n (A' ∩ B') = n (A U B)'

n (A' ∩ B') = 250 (Ans.)

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