Question

Let A and B be two sets such that n(A)=16, n(B)=14, n(A∪B) =25. Then,n(A∩B) is

equal to

(a) 30 (b)50 (c)5 (d)none of these​

Answer 1

Answer:

5 is your answer

Step-by-step explanation:

i hope it is helpful for you

Answer 2

The value of n(A∩B) = 5

Given :

A and B be two sets such that n(A) = 16 , n(B) = 14 , n(A∪B) = 25

To find :

The value of n(A∩B) is

(a) 30

(b) 50

(c) 5

(d) none of these

Formula :

For two sets A and B

n( A ∪ B ) = n(A) + n(B) - n( A ∩ B )

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that A and B be two sets such that n(A) = 16 , n(B) = 14 , n(A∪B) = 25

Step 2 of 2 :

Find the value of n(A∩B)

We are aware of the formula on set theory that

n( A ∪ B ) = n(A) + n(B) - n( A ∩ B )

⇒ 25 = 16 + 14 - n(A∩B)

⇒ n(A∩B) = 16 + 14 - 25

⇒ n(A∩B) = 30 - 25

⇒ n(A∩B) = 5

Hence the correct option is (c) 5

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