Disjoint unions

#IE#disjoint#sum

Statement

Show that if $A\cap B=\emptyset$ , then $|A\cup B|=|A|+|B|$ .

Hint

Disjoint case of IE.

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IE. $|A\cup B|=|A|+|B|-|A\cap B|=|A|+|B|-0$ .

Conclusion. The disjoint case reduces to the sum rule.