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Question

For 2 sets A and B, which of the following is/are true always?


A

A - B = {x : x A and x B}

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B

The sets A - B, A B and B - A are mutually disjoint sets.

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C

A - B = B - A

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D

A B = {x : x B and x A}

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Solution

The correct options are
A

A - B = {x : x A and x B}


B

The sets A - B, A B and B - A are mutually disjoint sets.


(a) A - B is the set in which elements belong to A, but does not belong to B. So, A - B = {x : x A and x B}.

(b)

So, A - B, A B and B - A are mutually disjoint sets.

(c) As A - B and B - A are disjoint sets, A - B B - A always.

(d) A B = {x : x A or x B}

So, only first two options are true.


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