# 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.

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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Obiajulu

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
$$A\cap B = \{1,2,3\}. ​$$