Question

If X and Y are two sets such that X ∪ Y has 50 elements, X has

28 elements and Y has 32 elements, how many elements does X ∩ Y have ?​

Answer 1

Step-by-step explanation:

Given n(X∪Y) = 50; n(X) = 28; n(Y) = 32

But n(X∪Y) = n(x) + n(y)-n(X∩Y)

n(X∩Y) = 28 + 32-50 =

= 60 - 50 = 10

Answer 2

Step-by-step explanation:

It is given that:

n(X∪Y)=18,n(X)=8,n(Y)=15

n(X∩Y)=?

We know that:

n(X∪Y)=n(X)+n(Y)−n(X∩Y)

∴18=8+15−n(X∩Y)

⇒n(X∩Y)=23−18=5

∴n(X∩Y)=5