Question

If A and B are two sets such that n(A)=35, n(B)=30 and n(U)=50 then the least value of n(A⋂B)=?

Answer 1

n(AUB)=n(A)+n(B)-n(A⋂B)

so for n(A⋂B) to be least n(AUB) should be maximum which is when n(AUB)=n(U)=50

thus,

50=35+30-n(A⋂B)

n(A⋂B)=15.

value of n(A⋂B) cannot be lesser than this as that would mean n(AUB)>n(U) which is not possible.

**Answer=15**

Answer 2

Answer: n(A ∩ B) is 15

Step-by-step explanation:

• This is an question of set theory.
• We know n(A U B)=n(A)+n(B)-n(A ∩ B)
• Given, n(A)=35, n(B)=30 and n(U)=50
• Now, n(A ∩ B)=n(A)+n(B)-n(A U B)

              ⇒ n(A ∩ B)=30+35-50

              ⇒ n(A ∩ B)=65-50

              ∴  n(A ∩ B)=15

• So,  n(A ∩ B) is 15.
• Hence, the required answer is 15.

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