# Prove or Disprove: For all sets A and B, |A

Prove or Disprove: For all sets $$\displaystyle{A}{\quad\text{and}\quad}{B},{\left|{A}\cup{B}\right|}={\left|{A}\right|}+{\left|{B}\right|}$$

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sweererlirumeX
Given statment is false.
Suppose A = {1,2,3,4,5}
B = {1,2,6,7,8}
$$\displaystyle\Rightarrow{A}\cup{B}={\left\lbrace{1},{2},{3},{4},{5},{6},{7},{8}\right\rbrace}$$
$$\displaystyle\Rightarrow{\mid}{A}\cup{B}={8}$$
$$\displaystyle{f}{\left|{A}\right|}={5},{\left|{B}\right|}={5}$$
$$\displaystyle\therefore{\left|{A}\right|}+{\left|{B}\right|}={10}$$
$$\displaystyle\therefore{\left|{A}\cup{B}\right|}\leq{\left|{A}\right|}+{\left|{B}\right|}$$