Question

For three sets $A,B$ and $C,A\cap (B-C)=$

• A. $A\cap B\cap C$
• B. $(A\cap B)-(A\cap C)$
• C. $(A\cap B)\cup (A\cap C)$
• D. $A\cup B\cup C$

Answer 1

The correct option is B $(A\cap B)-(A\cap C)$

$A\cap (B-C)$
$=A\cap (B\cap C^{\prime })$
$=(A\cap B)\cap C^{\prime }$
$=\varphi \cup \left[\right(A\cap B)\cap C^{\prime }]$
$=\left[\right(A\cap B)\cap A^{\prime }]\cup \left[\right(A\cap B)\cap C^{\prime }]$
$=(A\cap B)\cap (A^{\prime }\cup C^{\prime })$
$=(A\cap B)\cap (A\cap C{)}^{\prime }$
$=(A\cap B)-(A\cap C)$