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,\(\displaystyle{n}{\left({\left({A}{U}{B}\right)}\cap{C}\right)}={7}\)

\(\displaystyle{U}={\left\lbrace{10},{11},{12},{13},{14},{15},{16},{17},{18},{19},{20}\right\rbrace}\)

\(\displaystyle{A}={\left\lbrace{10},{12},{14},{16},{18},{20}\right\rbrace}\)

\(\displaystyle{B}={\left\lbrace{12},{15}\right\rbrace}\)

\(\displaystyle{C}={\left\lbrace{10},{12},{14},{15},{16},{18},{20}\right\rbrace}\)

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,\(\displaystyle{n}{\left({\left({A}{U}{B}\right)}\cap{C}\right)}={7}\)