Question

If $AandB$ are two disjoint sets, then which one of the following is correct?

• A. $A-B=A-(A\cap B)$
• B. $B-A=A\cap B$
• C. $A\cap B=(A\cup B)$
• D. none of these

Answer 1

The correct option is A

$A-B=A-(A\cap B)$

Explanation for the correct option:
Given that $AandB$ are two disjoints.

Therefore, $A\cap B=Ø$

Now, $\begin{array}{rcl}A–B& =& A\end{array}$

And $\begin{array}{rcl}A–(A\cap B)& =& A–Ø\\ & =& A\end{array}$

Thus $A–B=A–(A\cap B)$

Hence option A is the correct answer.