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Sets — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSets5 Marks
Question
Find sets A, B and C such that $\text{A}\cap\text{B},\text{ A}\cap\text{C and B}\cap\text{C}$ are non-empty sets and $\text{A}\cap\text{B}\cap\text{C}=\phi.$
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Answer

To find sets A, B and C such that $\text{A}\cap\text{B}\not=\phi,\ \text{A}\cap\text{C}=\phi$ and $\text{B}\cap\text{C}=\phi,\text{ and }\text{A}\cap\text{B}\cap\text{C}=\phi$
Take $\text{A} = \{1, 2, 3\}$
$\text{B} = \{2, 4, 6\}$
and $\text{C} = \{3, 4, 7\}$
Then,
$\text{A}\cap\text{B}=\{2\}$
$\therefore\text{A}\cap\text{B}\not=\phi$
$\text{A}\cap\text{C}=\{3\}$
$\therefore\text{A}\cap\text{C}\not=\phi$
$\text{B}\cap\text{C}=\{4\}$
$\therefore\text{B}\cap\text{C}\not=\phi$
However A, B and C have no elements in common,
$\therefore\text{A}\cap\text{B}\not=\phi.$

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