Set theory jee main

Question

If n(U)=60,n(A)=35,n(B)=24 and n(A∪B)′=10 ,then n(A∩B) is

• A. 9
• B. 8
• C. 6
• D. 7

Answer 1

Correct option: (A) 9

we have formula, 

n ( A ∪ B ) = n ( U ) − n ( A ∪ B ) ′ 

n ( A ∪ B ) = 60 − 10 = 50 

Now, 

n ( A ∪ B ) = n ( A ) + n ( B ) − n ( A ∩ B ) 

50 = 35 + 24 − n ( A ∩ B ) 

∴ n ( A ∩ B ) = 9