Question

If $A=\{1,2,3,4,5\},B=\{2,4,6,8\}$ and C= $\{3,4,5,6\}$,

then verify : $A-(B\cup C)=(A-B)\cap (A-C)$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, $A=\{1,2,3,4,5\},B=\{2,4,6,8\}$ and $C=\{3,4,5,6\}$

For the LHS:

Union of two sets will have the elements of both sets.

So, $B\cup C=\{2,3,4,5,6,8\}$

$A-(B\cup C)$ will have elements of $A$ which are not in $(B\cup C)$

So, $A-(B\cup C)=\left\{1\right\}$ ..... $\left(1\right)$

For the RHS:

$A-B$ will have elements of $A$ which are not in $B$.

So, $A-B=\{1,3,5\}$

$A-C$ will have elements of $A$ which are not in $C$.

So, $A-C=\{1,2\}$

Intersection of two sets has the common elements of both the sets.

$\Rightarrow (A-B)\cap (A-C)=\left\{1\right\}$ ..... $\left(2\right)$

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

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

Hence, the given expression is true.