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Difference of Two Sets

If A and B ar...

Question

If A and B are subsets of a set X, then A - B is ___________ .

A

$A - B = A \cup B$

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B

$A - B = A \cap B$

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C

$A - B = A^{'} \cap B$

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D

$A - B = A \cap B^{'}$

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Solution

The correct option is D
$A - B = A \cap B^{'}$

$A - B = {x : x ϵ A a n d x \notin B}$
$= {x : x ϵ A a n d x \in B^{'}} = A \cap B^{'}$

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