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1. Suppose A, B and C are sets. Prove that (A \ B) U (A\ C) = A\ (Bn C). [Prove this using elements of these sets – no Venn diagrams!]

1. Suppose A, B and C are sets. Prove that (A \ B) U (A\ C) = A\ (Bn C). [Prove this using elements of these sets – no Venn diagrams!]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Suppose A, B and C are sets. Prove that (A\ B) U (A\ C) = A\ (Bn C). [Prove this using elements of these sets – no Venn diagrams!] 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B) U C) \ D, An(BU C) \ D, An(BU(C\ D)) (+) are all different. (Justify your answer by saying exactly what the four sets in (-) are.) 3. Suppose a, n e Z and 0 < a < n. Prove that O-(".")-C) 1 + а- 1 = a in two different ways: firstly using the formula for in terms of factorials; and secondly by consid- ering subsets of {1,..., n}.
Transcribed Image Text:1. Suppose A, B and C are sets. Prove that (A\ B) U (A\ C) = A\ (Bn C). [Prove this using elements of these sets – no Venn diagrams!] 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B) U C) \ D, An(BU C) \ D, An(BU(C\ D)) (+) are all different. (Justify your answer by saying exactly what the four sets in (-) are.) 3. Suppose a, n e Z and 0 < a < n. Prove that O-(".")-C) 1 + а- 1 = a in two different ways: firstly using the formula for in terms of factorials; and secondly by consid- ering subsets of {1,..., n}.
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