Question

If $A=\{x:x\text{is a multiple of}3\}$ and $B=\{x:x\text{is a multiple of}5\}$, then $A-B=$

• A. $A^C\cap B$
• B. $A\cap B^C$
• C. $A^C\cap B^C$
• D. $(A\cap B{)}^C$

Answer 1

The correct option is B $A\cap B^C$

$A-B=A-A\cap B$
$A\cap B=\{x:x\text{is a multiple of}15\}$
Let $S$ be the universal set.
Then $A\cap S=A$
$\therefore A-A\cap B=A\cap S-A\cap B=A\cap (S-B)=A\cap B^C$