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. Find (A'UC) - B

Factors and multiples
ANSWERED
asked 2021-07-30
\(\displaystyle{U}=\) 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 \(\displaystyle{\left({A}'{U}{C}\right)}-{B}\)

Answers (1)

2021-07-31
Step 1
\(\displaystyle{U}=\) the set of natural numbers between 10 and 20.
\(\displaystyle{U}=\le{f}{t}{\left\lbrace{11},{12},{13},{14},{15},{16},{17},{18},{19}{r}{i}{g}{h}{t}\right\rbrace}\)
\(\displaystyle{A}=\) even numbers \(\displaystyle\Rightarrow\le{f}{t}{\left\lbrace{2},{4},{6},\ldots{18}{r}{i}{g}{h}{t}\right\rbrace}\)
\(\displaystyle{B}=\) multiples of three where the number 15 less than 18.
\(\displaystyle{B}=\le{f}{t}{\left\lbrace{3},{6},{9},{12},{15}{r}{i}{g}{h}{t}\right\rbrace}\)
\(\displaystyle{C}=\) composite numbers
\(\displaystyle=\le{f}{t}{\left\lbrace{4},{6},{8},{9},{10},{12},{14},{15},{16},{18},\ldots{r}{i}{g}{h}{t}\right\rbrace}\)
Step 2
Find \(\displaystyle{\left({A}'{U}{C}\right)}-{B}\)
Hence, \(\displaystyle{A}'=\le{f}{t}{\left\lbrace{1},{3},{5},{7},{9},{11},{13},\ldots{r}{i}{g}{h}{t}\right\rbrace}\)
Now, \(\displaystyle{\left({A}'{U}{C}\right)}=\le{f}{t}{\left\lbrace{1},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12},{13},{14},{15},{16},{17},{18},{19},\ldots{r}{i}{g}{h}{t}\right\rbrace}\)
and \(\displaystyle{\left({A}'{U}{C}\right)}-{B}=\le{f}{t}{\left\lbrace{1},{4},{5},{7},{8},{10},{11},{13},{14},{16},{17},{19}{r}{i}{g}{h}{t}\right\rbrace}\)
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