Question

# 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((AUB) \cap C)

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

2021-08-01
Given that,
$$\displaystyle{U}={\left\lbrace{10},{11},{12},{13},{14},{15},{16},{17},{18},{19},{20}\right\rbrace}$$
$$\displaystyle{A}={\left\lbrace{10},{12},{14},{16},{18},{20}\right\rbrace}$$
$$\displaystyle{B}={\left\lbrace{12},{15}\right\rbrace}$$
$$\displaystyle{C}={\left\lbrace{10},{12},{14},{15},{16},{18},{20}\right\rbrace}$$
Now, $$\displaystyle{\left({A}{U}{B}\right)}={\left\lbrace{10},{12},{14},{16},{18},{20}\right\rbrace}{U}{\left\lbrace{12},{15}\right\rbrace}$$
$$\displaystyle{\left({A}{U}{B}\right)}={\left\lbrace{10},{12},{14},{15},{16},{18},{20}\right\rbrace}$$
$$\displaystyle\Rightarrow{\left({A}{U}{B}\right)}\cap{C}={\left\lbrace{10},{12},{14},{15},{16},{18},{20}\right\rbrace}\cap{\left\lbrace{10},{12},{14},{15},{16},{18},{20}\right\rbrace}$$
$$\displaystyle\Rightarrow{\left({A}{U}{B}\right)}\cap{C}={\left\lbrace{10},{12},{14},{15},{16},{18},{20}\right\rbrace}$$
$$\displaystyle\Rightarrow{n}{\left({\left({A}{U}{B}\right)}\cap{C}\right)}={7}$$
Hence,$$\displaystyle{n}{\left({\left({A}{U}{B}\right)}\cap{C}\right)}={7}$$