Proposition 10.2.1: (the addition principle)
Suppose that X and Y are disjoint finite sets. Then X U Y is finite and
|X UY| = |X| + |Y|.
Corollary 10.2.2:
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|.
Mathematics Homework Solutions
#54868
Induction and Set theory : Addition Principle, 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.
Addition Principle, Induction, Union and Pairwise Disjoint Finite Sets are investigated. The solution is detailed and well presented.
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