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Induction and Set theory : Union and Pairwise Disjoint Finite Sets

Proposition 10.2.1: (the addition principle)

Suppose that X and Y are disjoint finite sets. Then X U Y is finite and |X U Y| = |X| + |Y|.

Corollary 10.2.2:
For a positive integer n, suppose that X1, X2....,Xn is a collection of n pairwise disjoint finite sets (i.e. i does not = j => Xi Xj = empty set)

Then X1 U X2 U....U Xn = U ( lim from n to i=1) Xi is a finite set and
|X1 U X2 U......U Xn| = |X1| + |X2|+....|Xn|.

Please see the attached file for the fully formatted problems.


Solution Summary

Addition principle, induction, union and pairwise disjoint finite sets are investigated and discussed. The solution is detailed and well presented.