Wierzycaz

2021-07-31

$U=$ the set of natural numbers between 10 and 20
$A=$ Even Numbers
$B=$ Multiples of 3 where the number is less than 18.
$C=$ Composite numbers
Find $n\left(\left(AUB\right)\cap C\right)$

### Answer & Explanation

Cristiano Sears

Given that,
$U=\left\{10,11,12,13,14,15,16,17,18,19,20\right\}$
$A=\left\{10,12,14,16,18,20\right\}$
$B=\left\{12,15\right\}$
$C=\left\{10,12,14,15,16,18,20\right\}$
Now, $\left(AUB\right)=\left\{10,12,14,16,18,20\right\}U\left\{12,15\right\}$
$\left(AUB\right)=\left\{10,12,14,15,16,18,20\right\}$
$⇒\left(AUB\right)\cap C=\left\{10,12,14,15,16,18,20\right\}\cap \left\{10,12,14,15,16,18,20\right\}$
$⇒\left(AUB\right)\cap C=\left\{10,12,14,15,16,18,20\right\}$
$⇒n\left(\left(AUB\right)\cap C\right)=7$
Hence,$n\left(\left(AUB\right)\cap C\right)=7$

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