Question

If $A$ and $B$ be subsets of a set $X$. Then

• A. $A–B=A\cup B$
• B. $A–B=A\cap B$
• C. $A–B=A^c\cap B$
• D. $A–B=A\cap B^c$

Answer 1

The correct option is D

$A–B=A\cap B^c$

Explanation for the correct option:

$\begin{array}{rcl}A-B& =& \left\{x:x\in Aandx\notin B\right\}\\ & =& \left\{x:x\in Aandx\in B^c\right\}\\ & =& A\cap B^{\mathrm{c}}\end{array}$

Hence, Option ‘D’ is Correct.