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Let A, B, C, and D be subsets of a universal set U. 3. (a) Prove that if A C B, then BCA (b) Prove that (Ax C) U (B x D) C (AU B) x (CU D) (c) Let P(X) denote the power set of a set X. Prove or disprove: P(An B) P(A) n P(B) (d) Prove or disprove: (AUB) x (C U D) (Ax C) U (B x D)

Let A, B, C, and D be subsets of a universal set U. 3. (a) Prove that if A C B, then BCA (b) Prove that (Ax C) U (B x D) C (AU B) x (CU D) (c) Let P(X) denote the power set of a set X. Prove or disprove: P(An B) P(A) n P(B) (d) Prove or disprove: (AUB) x (C U D) (Ax C) U (B x D)

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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Let A, B, C, and D be subsets of a universal set U. 3. (a) Prove that if A C B, then BCA (b) Prove that (Ax C) U (B x D) C (AU B) x (CU D) (c) Let P(X) denote the power set of a set X. Prove or disprove: P(An B) P(A) n P(B) (d) Prove or disprove: (AUB) x (C U D) (Ax C) U (B x D)
Transcribed Image Text:Let A, B, C, and D be subsets of a universal set U. 3. (a) Prove that if A C B, then BCA (b) Prove that (Ax C) U (B x D) C (AU B) x (CU D) (c) Let P(X) denote the power set of a set X. Prove or disprove: P(An B) P(A) n P(B) (d) Prove or disprove: (AUB) x (C U D) (Ax C) U (B x D)
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