Question

If X and Y are two sets such that X has 40 elements, X ∪Y has 60 elements and X ∩Y has 10 elements, how many elements does Y have?​

Answer 1

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We know that

n(X) = 40

n(X ∪ Y) = 60

n(X ∩ Y) = 10

It can be written as

n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)

By substituting the values

60 = 40 + n(Y) – 10

On further calculation

n(Y) = 60 – (40 – 10) = 30

Therefore,

the set Y has 30 elements.

Answer 2

Step-by-step explanation:

Given-

n(X) = 40, n(X ∩ Y) = 10, and n(X ∪ Y) = 60

We know that-

n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)

⇒ 60 = 40+n(Y) - 10

⇒ 60 = 30+n(Y)

⇒ n(Y) = 60-30

∴ n(Y) = 30

Thus, the no. of elements in n(Y) is 30.