prove its true: |AUB|=|A|+|B|-|Aintersection B|

[OSMAN]

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[HallsofIvy]

Divide A and B into three sets: all x that are in A but not B, all y that are in B but not A, all z that are in \(\displaystyle A\cap B\). Show that that every member of A and B is in one and only one of those.

 

[pka]

Prove \(\displaystyle |A\cup B|=|A|+|B|-|A\cap B|\)

If \(\displaystyle X,~Y,~\&~Z \) are three pairwise disjoint sets then \(\displaystyle |X\cup Y\cup Z|=|X|+|Y|+|Z|\)
\(\displaystyle |(A\setminus B)|=|A|-|A\cap B| \)

If you understand that the show that \(\displaystyle (A\cup B)=(A\setminus B)\cup (B\setminus A)\cup (A\cap B) \)