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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 nite 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 nite 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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This note was uploaded on 10/15/2011 for the course MATH 23b taught by Professor Bonglian during the Spring '09 term at Brandeis.
- Spring '09