Question

(i) $A-(B-C)=(A-B)\cup (A\cap C)$
(ii) $A-B=(A\cup B)-B=A-(A\cap B)$
Verify these equalities if
$A=\{1,2,3,4,5,6,7\},B=\{3,5,6,7,9,11\}$
and $C=\{2,5,6,9,20\}$

Answer 1

Ans. True.
(i) $A-(B-C)=A-(B\cap C^{\prime })$
$A\cap {(B\cap C^{\prime })}^{\prime }$
$A\cap (B^{\prime }\cup C)=A\cap B^{\prime }\cup (A\cap C)$
$(A-B)\cup (A\cap C)$
(ii) $(A\cup B)-B=(A\cup B)\cap B^{\prime }$
$(A\cap B^{\prime })\cup (B\cap \overline{B^{\prime }})$
$(A\cap B^{\prime })\cup \varphi$
$A\cap B^{\prime }=A-B$ etc.