Given statment is false.

Suppose A = {1,2,3,4,5}

B = {1,2,6,7,8}

\(\displaystyle\Rightarrow{A}\cup{B}={\left\lbrace{1},{2},{3},{4},{5},{6},{7},{8}\right\rbrace}\)

\(\displaystyle\Rightarrow{\mid}{A}\cup{B}={8}\)

\(\displaystyle{f}{\left|{A}\right|}={5},{\left|{B}\right|}={5}\)

\(\displaystyle\therefore{\left|{A}\right|}+{\left|{B}\right|}={10}\)

\(\displaystyle\therefore{\left|{A}\cup{B}\right|}\leq{\left|{A}\right|}+{\left|{B}\right|}\)

Suppose A = {1,2,3,4,5}

B = {1,2,6,7,8}

\(\displaystyle\Rightarrow{A}\cup{B}={\left\lbrace{1},{2},{3},{4},{5},{6},{7},{8}\right\rbrace}\)

\(\displaystyle\Rightarrow{\mid}{A}\cup{B}={8}\)

\(\displaystyle{f}{\left|{A}\right|}={5},{\left|{B}\right|}={5}\)

\(\displaystyle\therefore{\left|{A}\right|}+{\left|{B}\right|}={10}\)

\(\displaystyle\therefore{\left|{A}\cup{B}\right|}\leq{\left|{A}\right|}+{\left|{B}\right|}\)