Question

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

• A. A - B = {x: x ∈ A and x ∉ B}
• B. The sets A - B, A ∩ B and B - A are mutually disjoint sets.
• C. A - B = B - A
• D. A ∪ B = {x: x ∈ B and x ∉ A}

Answer 1

Answer: (A), (B)

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 belongs to A but not belong to B.

So, $A-B=x:xϵAandx\notin B$

(b)

So, $A-B,A\cap B$ and $B-A$ are mutually disjoint sets

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

(d) $A\cup B=x:xϵAorxϵB$

So, only options A and B are true