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in Mathematics by (57.5k points)

If A, B and C are three sets and U is the universal set such that n(U) = 700, n(A) = 200 , n(B) = 300 and n(A ∩ B) = 100, then what is the value of (A' ∩ B′) ? 

(a) 100 

(b) 200 

(c) 300 

(d) 400 

1 Answer

+1 vote
by (63.7k points)
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Best answer

Correct option is (c) 300

Explanation:

Given that, n(U) = 700, n(A) = 200, n(B) = 300 

and n(A ∩ B) = 100 

We know that,

 n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

= 200 + 300 - 100 = 400

 Now, n(A' ∩ B′) = n(U) - n(A ∪ B)

=700 - 400 = 300

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