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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets3 Marks
Question
If A and B are two sets such that $\text{n}(\text{A}\cup\text{B})=50,\text{n(A)} = 28$ and $\text{n(B)} = 32,$ find $\text{n(A}\cap\text{B}).$
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Answer

$\text{n}(\text{A}\cup\text{B})=50,\text{n(A)= 28 and n(B)} = 32,$ where n(X) does not the cardinal number of the set x. We know that $\text{n}(\text{A}\cup\text{B})=\text{n(A)+n(B)-n(A}\cap\text{B)}$ $\Rightarrow50=28+32-\text{n(A}\cap\text{B})$ $\Rightarrow50=60-\text{n(A}\cap\text{B})$ $\Rightarrow\text{n(A}\cap\text{B})=60-50$ $= 10$ $\therefore\text{n(A}\cap\text{B})=10.$

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