Question

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

Then find : $A-(B\cap C)-(A-B)\cup (A-C).$

Answer 1

For the LHS:

Intersection of two sets has the common elements of both sets.
So, $B\cap C=$ { $4,6$ }

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

So, $A-(B\cap C)=$ { $1,2,3,5$ } .....(1)

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

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

$\Rightarrow (A-B)\cup (A-C)=$ { $1,2,3,5$ } ....(2)

From (1) and (2), we have,

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

$A-(B\cap C)-(A-B)\cup (A-C)=0$