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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets3 Marks
Question
For any two sets, prove that: $\text{A}\cap(\text{A}\cup\text{B})=\text{A}.$
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Answer

$\text{A}\cap(\text{A}\cup\text{B})=(\text{A}\cap\text{A})\cup(\text{A}\cap\text{B})$ $[\because\cap$ is distributive over $\cup]$ $=\text{A}\cup(\text{A}\cap\text{B})$ $[\because\text{A}\cap\text{A}=\text{A}]$ $=\text{A [using (i)]}.$

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