Question

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

• A. $A-B=\{x:x\in A\text{and}x\notin B\}$
• B. The sets $A-B,A\cap B\text{and}B-A$ are mutually disjoint sets.
• C. $A-B=B-A$
• D. $A\cup B=\{x:x\in B\text{and}x\notin A\}$

Answer 1

Answer: (A), (B)

The sets $A-B,A\cap B\text{and}B-A$ are mutually disjoint sets.

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

(b)

So,$A-B,A\cap B\text{and}B-A$ are mutually disjoint sets.

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

(d) $A\cup B=\{x:x\in A\text{or}x\in B\}$

So, only first two options are true.