Question

Given $U=\{x:x\in N,x\le 9\}$, $A=\{x:xisdivisibleby2$} and B $=\{x:\frac{x}{3}\in N\}$, then (A $\cup$ B) - (A $\cap$B) = ___.

• A. {2, 3, 4, 6, 8, 9}
• B. {2, 3, 4, 8, 9}
• C. {C}
• D. {2, 4, 6, 8}

Answer 1

The correct option is B

{2, 3, 4, 8, 9}

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

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

$A=\{x:xisdivisibleby2$}

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

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

$\Rightarrow B=\{3,6,9\}$

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 A and B

$\Rightarrow A\cap B=\left\{6\right\}$

$(A\cup B)-(A\cap B)$ is the set of elements belonging to only (A $\cup$ B)

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

= {2, 3, 4, 8, 9}

Hence (B)