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
ANSWERED
asked 2021-07-31
\(\displaystyle{U}=\) 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 \(\displaystyle{n}{\left({\left({A}{U}{B}\right)}\cap{C}\right)}\)

Expert Answers (1)

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