Question

For 2 sets A and B, which of the following is/are not true?

• A. $A-B=x:xϵAandx\mathrm{ϵ/}B$
• B. The sets $A-B,A\cap B$ and $B-A$ are mutually disjoint sets.
• C. $A-B=B-A$
• D. $A\cup B=x:xϵBandx\mathrm{ϵ/}A$

Answer 1

Answer: (C), (D)

The correct options are
C $A-B=B-A$
D $A\cup B=x:xϵBandx\mathrm{ϵ/}A$

(a) A - B is the set in which elements belongs to A but not belong to B.

So, $A-B=x:xϵAandx\mathrm{ϵ/}B$

(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.