Unformatted text preview: y 1 ,y 2 ∈ R , assume that f-1 ( y 1 ) ≤ f-2 ( y 2 ), and then argue that y 1 ≤ y 2 .) 4. Let m,n ∈ N , and A , B be disjoint ﬁnite sets. Let f : [ m ] → A and g : [ n ] → B be bijections. In no more than 20 lines, give a bijection h : [ m + n ] → A ∪ B ; you must prove that the h you give, is a bijection. (Experiment with the case m = 2, n = 3.) 5. Let A and B be ﬁnite sets, whose cardinalities are m,n ∈ N respectively. In no more than 10 lines, prove that the cardinality of A ∪ B does not exceed m + n . (Note that A ∪ B = A ∪ ( B-A ); A and B-A are disjoint; B-A ⊂ B .) 6. Problem 1 Page 95....
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- Spring '09
- Math, finite sets, complete sentences, Bijection, disjoint finite sets