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# Induction and Set theory : Union and Pairwise Disjoint Finite Sets

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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|.

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© BrainMass Inc. brainmass.com October 16, 2018, 5:29 pm ad1c9bdddf
https://brainmass.com/math/discrete-math/induction-set-theory-union-pairwise-disjoint-finite-sets-54868

#### Solution Summary

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

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