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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets4 Marks
Question
For three sets A, B and C, show that.
$\text{A}\cap\text{B}=\text{A}\cap\text{C}$ need not imply B = C.
✓

Answer

Let A = {1, 2, 3}, B = {2, 4, 6} and C = {2, 5, 7}
Then,
$\text{A}\cap\text{B}=\{2\}$
and $\text{A}\cap\text{C}=\{2\}$
Hence, $\text{A}\cap\text{B}=\text{A}\cap\text{C},$ but clearly $\text{B}\not=\text{C}.$

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