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Problem 1: Prove A = {m E Z : m mod 6 = 2} is a proper subset of B = {n € Z : n is even}. Problem 2: Shade a Venn diagram to represent the sets A, B, and C, such that: (i) C – (Aº n B) (ii) AN B = Ø and AnC= C Problem 3: Use the set identities/laws to show (A – Bº) U (A° U B)° = A. Problem 4: Recall that the power set P(A) is the set of all subsets of A. Prove that if AC BNC and B C C, then P(A) U P(B) C P(C).

Problem 1: Prove A = {m E Z : m mod 6 = 2} is a proper subset of B = {n € Z : n is even}. Problem 2: Shade a Venn diagram to represent the sets A, B, and C, such that: (i) C – (Aº n B) (ii) AN B = Ø and AnC= C Problem 3: Use the set identities/laws to show (A – Bº) U (A° U B)° = A. Problem 4: Recall that the power set P(A) is the set of all subsets of A. Prove that if AC BNC and B C C, then P(A) U P(B) C P(C).

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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Problem 1: Prove A = {m E Z : m mod 6 = 2} is a proper subset of B = {n € Z : n is even}. Problem 2: Shade a Venn diagram to represent the sets A, B, and C, such that: (i) C – (Aº n B) (ii) AN B = Ø and AnC= C Problem 3: Use the set identities/laws to show (A – Bº) U (A° U B)° = A. Problem 4: Recall that the power set P(A) is the set of all subsets of A. Prove that if AC BNC and B C C, then P(A) U P(B) C P(C).
Transcribed Image Text:Problem 1: Prove A = {m E Z : m mod 6 = 2} is a proper subset of B = {n € Z : n is even}. Problem 2: Shade a Venn diagram to represent the sets A, B, and C, such that: (i) C – (Aº n B) (ii) AN B = Ø and AnC= C Problem 3: Use the set identities/laws to show (A – Bº) U (A° U B)° = A. Problem 4: Recall that the power set P(A) is the set of all subsets of A. Prove that if AC BNC and B C C, then P(A) U P(B) C P(C).
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