Question

If n(A)=7 ,n(B)=9 and n(A U B )=14 then n(A ∩ B) =______________ *

Answer 1

Answer:

n(A U B) = n(A) + n(B) - n(A ∩ B)

14 = 7+ 9 -x

x = 16- 14

x = 2 ans

Answer 2

The value of n(A ∩ B) = 2

Given :

n(A) = 7 , n(B) = 9 and n(A ∪ B) = 14

To find :

The value of n(A ∩ B)

Formula :

We are aware of the formula on set theory that

n(A ∪ B) = n(A) + n(B) - n( A ∩ B)

Solution :

Step 1 of 2 :

Write down the given values

Here it is given that n(A) = 7 , n(B) = 9 and n(A ∪ B) = 14

Step 2 of 2 :

Find the value of n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ 14 = 7 + 9 - n(A ∩ B)

⇒ n(A ∩ B) = 7 + 9 - 14

⇒ n(A ∩ B) = 16 - 14

⇒ n(A ∩ B) = 2

Hence the value of n(A ∩ B) = 2

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