Question

If n(A)=11, n(B)=7, n(A U B)=13, then n(A n B)=?

Answer 1

Step-by-step explanation:

since,

n(AnB) =n(A) +n(B)-n(AUB)

=11+7-13

n(AnB) =5 is right answer

Answer 2

Answer:

5

Step-by-step explanation:

Concept= Set operations

Given= The values of few relation

To Find= The value of intersection

Explanation=

We have been given the question as, If n(A)=11, n(B)=7, n(A U B)=13, then n(A n B)=?

So we know the value of n(A),n(B) and n(A∪B).

n(A) = 11

n(B) = 7

n(A∪B) = 13

According to the relations in sets we know that in the Set of X and Y

X∪Y= X + Y - X∩Y

and in cardinal form we have it as ,

n(X∪Y )= n(X) + n(Y) - n(X∩Y)

So here we are given the sets as A and B so,

n(A∪B )= n(A) + n(B) - n(A∩B)

We know the values of n(A),n(B) and n(A∪B) so replacing it in the formula we have,

13 = 11 + 7 -n(A∩B)

13= 18 - n(A∩B)

n(A∩B)= 18-13

n(A∩B)= 5.

Therefore the value of n(A∩B) is 5.

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