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SETS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSETS1 Mark
Question
If X and Y are two sets such that X $\cup$Y has 50 elements, X has 28 elements, and Y has 32 elements, how many elements does X $\cap$ Y have?
✓

Answer

Here,
n (X $\cup$Y) = 50, n (X) = 28, n (Y) = 32,
n (X $\cap$Y) = ?
By using the formula,we have
n (X $\cup$Y) = n (X) + n (Y) – n (X $\cap$Y),
we find that
n (X $\cap$Y) = n (X) + n (Y) – n (X $\cup$Y)
= 28 + 32 – 50 = 10

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