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$|A_1 ∪ A_2 ∪···∪ A_m|=|A_1|+|A_2|+···+|A_m|$ when $A_i ∩ A_j = \emptyset$ for all $i,j$.

I understand that these are pairwise disjoint sets, and the number of ways to choose an element from one of the sets is the sum of the elements of the set. However, what does that "$A_i ∩ A_j = \emptyset$ for all $i,j$" at the end mean? for all $i,j$?

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    do you mean $A_i \cap A_j = \emptyset$ for all $i,j$? – 2017-01-20
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    If they're pairwise disjoint, this is most likely a typo and should say $A_i\cap A_j = \emptyset$ for all $i,j$. – 2017-01-20
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    In general $|A_1\cup A_2\cup \dots \cup A_m|=|A_1|+|A_2|+\dots+|A_m|$ iff $A_i\cap A_j = \color{red}{\emptyset}$ for all $i\neq j$ – 2017-01-20
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    @ Stahl @ JMoravitz thanks, guys. – 2017-01-20

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