Question

Given $U=\{x:x\in N,x\le 9\},$ $A=\{x:x\text{is divisible by 2}\}$ and $B=\{x:\frac{x}{3}\in N\},$ where $U$ is the universal set. Then, $(A\cup B)-(A\cap B)$ = ____. (3 mark)

Answer 1

$U=\{x:x\in N,x\le 9\}$

$\Rightarrow$ $U=\{1,2,3,4,5,6,7,8,9\}$

$A=\{x:x\text{is divisible by 2}}$

$\Rightarrow A=\{2,4,6,8\}$

$B=\{x:\frac{x}{3}\in N\}$

$\Rightarrow B=\{3,6,9\}$ (1 mark)

$A\cup B$ is the set of elements belonging to A or B.

$\Rightarrow A\cup B=\{2,3,4,6,8,9\}$

$A\cap B$ is the set of elements belonging to both A and B.

$\Rightarrow A\cap B=\left\{6\right\}$ (1 mark)

$(A\cup B)-(A\cap B)$ is the set of elements belonging to only $A\cup B$, and not $(A\cap B).$

$\therefore (A\cup B)-(A\cap B)=\{2,3,4,6,8,9\}-\left\{6\right\}$

$=\{2,3,4,8,9\}$ (1 mark)