Chpts_2,3_S08 - FOUNDATIONS OF ANALYSIS SPRING 2008...

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Unformatted text preview: FOUNDATIONS OF ANALYSIS SPRING 2008 TRUE/FALSE QUESTIONS SETS & FUNCTIONS Chapters #2 and #3 (1) A proper subset of a subset of a set, S , is a proper subset of S . (2) The union of two non-empty sets is non-empty. (3) The intersection of two non-empty sets is non-empty. (4) If the set, A , is a proper subset of the set, B , the complement of A in B is non-empty. (5) The empty set is a proper subset of the empty set. (6) Every set is a subset of itself. (7) If two sets are disjoint their union is the emptyset. (8) Let A denote a subset of the set U . Then x ∈ U \ A ⇔ ( x ∈ U ) ∧ ( x 6∈ A ) . (9) Let A and B denote subsets of a set U . Then ( A ∪ B ) c = A c ∩ B c . (10) Let A and B denote subsets of a set U . Then ( A ∩ B ) c = A c ∪ B c . (11) Let S and T denote non-empty sets. Let f : S onto → T and g : T onto → S . Then f and g are both 1-1 functions. 1 (12) Let S and T denote non-empty sets. Let f : S 1- 1 → T . Then the inverse function, f- 1 , is defined on...
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This note was uploaded on 04/07/2008 for the course MATH Foundation taught by Professor Kiehl during the Spring '08 term at Rensselaer Polytechnic Institute.

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Chpts_2,3_S08 - FOUNDATIONS OF ANALYSIS SPRING 2008...

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