# If X and Y are two sets such that n(X) = 23, n(Y) = 39, and n(XUY) = 49, then find n(X∩Y).

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MP HSTET Varg 1 - 2018 (Hindi) Held on 2nd Feb 2019 Shift 2
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1. 13
2. 10
3. 12
4. 11

## Answer (Detailed Solution Below)

Option 1 : 13
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## Detailed Solution

Given:

n(X) = 23, n(Y) = 39, and n(XUY) = 49

To find:  n(X∩Y).

Formula used:

n(XUY) = n(X) + n(Y) - n(X∩Y)

Calculation:

⇒ n(XUY) = n(X) + n(Y) - n(X∩Y)

⇒ 49 = 23 + 39 - n(P∩Z)

⇒ n(X∩Y = 23 + 39 - 49

⇒ n(X∩Y) = 62 - 49

⇒ n(X∩Y) = 13

Hence, the correct answer is "13".

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