Let A={x:xA={x:x is a natural number and a factor of 18}B={x:xB={x:x is a natural number and less than 6}Find Acup B and Acap B.

coexpennan 2021-02-25 Answered

Let \(\displaystyle{A}={\left\lbrace{x}:{x}{A}={\left\lbrace{x}:{x}\ {i}{s}\ {a}\ {n}{a}{t}{u}{r}{a}{l}\ nu{m}{b}{e}{r}{\quad\text{and}\quad}{a}\ {f}{a}{c}to{r}{\ o}{f}\ {18}\right\rbrace}\right.}\)
\(\displaystyle{B}={\left\lbrace{x}:{x}{B}={\left\lbrace{x}:{x}\ {i}{s}\ {a}\ {n}{a}{t}{u}{r}{a}{l}\ nu{m}{b}{e}{r}{\quad\text{and}\quad}\ le{s}{s}\ {t}{h}{a}{n}\ {6}\right\rbrace}\right.}\)
Find \(\displaystyle{A}\cup{B}{\quad\text{and}\quad}{A}\cap{B}.\)

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Expert Answer

Obiajulu
Answered 2021-02-26 Author has 24797 answers

Here \(\displaystyle{A}={\left\lbrace{x}\ {i}{s}\ {a}\ {n}{a}{t}{u}{r}{a}{l}\ nu{m}{b}{e}{r}{\quad\text{and}\quad}{f}{a}{c}to{r}\ {o}{f}\ {18}\right\rbrace}\).

\(={\left\lbrace{1},{2},{3},{6},{9},{18}\right\rbrace}{A}={\left\lbrace{x}\ {i}{s}\ {a}\ {n}{a}{t}{u}{r}{a}{l}\ nu{m}{b}{e}{r}{\quad\text{and}\quad}{f}{a}{c}to{r}\ {o}{f}\ {18}\right\rbrace}\)

\(={\left\lbrace{1},{2},{3},{6},{9},{18}\right\rbrace}{\quad\text{and}\quad}{B}={\left\lbrace{x}\ {i}{s}\ {a}\ {n}{a}{t}{u}{r}{a}{l}\ nu{m}{b}{e}{r}{\quad\text{and}\quad}\ le{s}{s}\ {t}{h}{a}{n}\ {6}\right\rbrace}\)

\(={\left\lbrace{1},{2},{3},{4},{5}\right\rbrace}.{B}={\left\lbrace{x}\ {i}{s}\ {a}\ {n}{a}{t}{u}{r}{a}{l}\ nu{m}{b}{e}{r}{\quad\text{and}\quad}\ le{s}{s}\ {t}{h}{a}{n}\ {6}\right\rbrace}={\left\lbrace{1},{2},{3},{4},{5}\right\rbrace}\)

Therefore,
\(A\cup B\ and A\cap B=\{1,2,3,4,5,6,9,18\}=\{1,2,3\}.\)
\(A\cup B = \{1,2,3,4,5,6,9,18\}\)
and
\(A\cap B = \{1,2,3\}. ​\)

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