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

geduiwelh 2021-08-12 Answered
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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Expert Answer

sweererlirumeX
Answered 2021-08-13 Author has 21793 answers
Given statment is false.
Suppose A = {1,2,3,4,5}
B = {1,2,6,7,8}
\(\displaystyle\Rightarrow{A}\cup{B}={\left\lbrace{1},{2},{3},{4},{5},{6},{7},{8}\right\rbrace}\)
\(\displaystyle\Rightarrow{\mid}{A}\cup{B}={8}\)
\(\displaystyle{f}{\left|{A}\right|}={5},{\left|{B}\right|}={5}\)
\(\displaystyle\therefore{\left|{A}\right|}+{\left|{B}\right|}={10}\)
\(\displaystyle\therefore{\left|{A}\cup{B}\right|}\leq{\left|{A}\right|}+{\left|{B}\right|}\)
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