Question

Given that set $A=${$x:x$ is aninteger that is divisible by $3,1\le x\le 10$} and $B=$ {$x/x$ is an even integer,$1\le x\le 10$}. If the universal set for $A$ and $B$ is $\mu$ where n$\left(\mu \right)=9$, which of
the following could be that set $\mu$?
${\mu }_1=\{1,2,3,4,5,6,7,8,9\}$
${\mu }_2=\{2,3,4,5,6,7,8,9,10\}$
${\mu }_3=\{1,2,3,4,5,7,8,9,10\}$

Enter $n$ for ${\mu }_n$.

Answer 1

Given that

$A=$ {$x:x$ is an integer that is divisible by $3$, $1\le x\le 10$}

So, $A=\{3,6,9\}$

$B=${$x:x$ is an even integer, $1\le x\le 10$}

So, $B=\{2,4,6,8,10\}$

Universal set for $A$ and $B$ is $\mu$

$n(\mu$) $=9$

There are $9$ elements in universal set $\mu$

$A\cup B=$ $\{2,3,4,6,8,9,10\}$

${\mu }_1$, contains $9$ elements but it does not contain $10$ in set

${\mu }_2$ contain $9$ element and it contain all element in both set $A$ and $B$.

Again ${\mu }_3$ contains $10$ elements so it is discarded since $n(\mu$) $=9$.

So, $u_2$ in the answer .