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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a3c358f-b20b-40b2-995a-508219fdfa64%2F4f48bc65-0a71-4afe-8cc5-abc6b75aaeac%2Fldhsmx_processed.png&w=3840&q=75)
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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