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Relations

Let A=1,2,3,4...

Question

Let $A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ and $B = {2, 3, 5, 7}$ .
Find $A \cap B$ and hence show that $A \cap B = B$ .

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Solution

Given: $A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ and
$B = {2, 3, 5, 7}$
$A \cap B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} \cap {2, 3, 5, 7}$
$\Rightarrow A \cap B = {2, 3, 5, 7}$
$\Rightarrow A \cap B = B$
Hence proved

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