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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets3 Marks
Question
If P and Q are two sets such that P has 40 elements, $\text{P}\cup\text{Q}$ has 60 elements and $\text{P}\cap\text{Q}$ has 10 elements, how many elements does Q have?
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Answer

We have,
$\text{n(P)} = 40,\text{n(P}\cup\text{Q)}=60,\text{ n(P}\cap\text{Q})=10,$ to find $\text{n(Q)}.$
$\Rightarrow60 = 40 + \text{n(Q)} - 10$
$\Rightarrow60 = 30 +\text{n(Q)}$
$\Rightarrow\text{n(Q)} = 60 - 30$
$= 30$
Hence, Q has 30 elements.

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