# Proof about union and cardinalities

Please help with the following problem. Provide a step by step explanation.

Show that given finite sets A_1, A_2,...,A_n, that are pairwise-disjoint, that is A_i intersection A_ j = empty set for all i not equal to j, then their union is a finite set and the cardinality of their union is the sum of the cardinalities of the sets:

#(A_1 union A_2 union...union A_n) = #A_1 + #A_2 +...+ # A_n

* Use that fact that the statement is true for n=2

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#### Solution Preview

Problem: Show that given finite sets A_1, A_2,...,A_n, that are pairwise-disjoint, that is A_i intersection A_ j = empty set for all i not equal to j, then their union is a finite set and the cardinality of their union is the sum of the cardinalities of the sets: #(A_1 union A_2 union...union A_n) = #A_1 + #A_2 +...+ # A_n. Use that fact that the ...

#### Solution Summary

This solution helps put together a proof about union and cardinalities. It helps prove that finite sets are pairwise-dispoint and that an intersection is a finite set. Step by step calculations are given.