Question

If $A=\{1,3,5,7,9\},B=\{1,2,3\}$ and $C=\{2,3,4\}$ .Verify:$A-(B\cup C)=(A-B)\cap (A-C)$

Answer 1

$B\cup C=\{1,2,3\}\cup \{2,3,4\}$ $=\{1,2,3,4\}$

$A-(B\cup C)=\{1,3,5,7,9\}-\{1,2,3,4\}$ $=\{5,7,9\}$

$\therefore A-(B\cup C)=\{5,7,9\}$ ........$\left(1\right)$

$A-B=\{1,3,5,7,9\}-\{1,2,3\}=\{5,7,9\}$

$A-C=\{1,3,5,7,9\}-\{2,3,4\}=\{1,5,7,9\}$

$(A-B)\cap (A-C)=\{5,7,9\}\cap \{1,5,7,9\}=\{5,7,9\}$

$\therefore (A-B)\cap (A-C)=\{5,7,9\}$ ........$\left(2\right)$

$\therefore$ From $\left(1\right)$ and $\left(2\right)$ we have

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

Hence verified.