**Problem 3:**Prove or disprove (you may use all of our set properties here, such as those from the Section 6.2 theorems): Given a universal set \( U \), for all sets \( A, B, C \subseteq U \), \[ A \cup (B - C) = (A \cup B) - (A \cup C) \].

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Answered: Problem 3: Prove or disprove (you may…

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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The universal set in these problems is U = {−10, −9, −8, . . . 18, 19, 20}. Note that this set is notsymmetric around 0.Define the following sets in universe:A = {−9, −7, −3, −2, 1, 7, 8, 16, 20}B = {x ∈ U : x ≤ 5}C = {x ∈ U : x is even}D = {x ∈ U : |x| ≥ 8}(a) List B, C and D in roster notation.
Question 1: Consider the universal set U {2,5,7), C= {1, 3, 5, 7, 9}. Find: (a) (An B) and (ANC) (d) AAB and AAC {1,2,3,,8,9} and sets A = (c) A and Ce (b) (AUB) and (BUC) (e) (AUC)\B and (BAC)\A {1,2,5, 6}, B = Question 2: In a survey of 160 peoples, it was found that: 105 read Newsweek magazine, 60 read both Newsweek and Time, 85 read Time, 65 read both Newsweek and Fortune, 72 read Fortune, 45 read both Time and Fortune, and 48 read all three magazines. Find: (a) Find the number of peoples who read exactly one magazine. (b) Find the number of peoples who read at least one of the three magazines. Question 3: A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of three popular options, air-conditioning (A), radio (R), and power windows (W), were already installed. The survey found: 15 had air-conditioning (A), 5 had A and 1 W, 12 had radio (R), 9 had A and 1 R, 11 had power windows (W), 4 had R and 1 W, and finally 3 had all three options.…
Please prove the statement below: For all sets X, Y, and Z subsets of a universal set U (X -- Y) ∩ (Z -- Y) = (X ∩ Z) -- Y Notes: 1. Use an element argument, see page 356 in the textbook.
Do not use Venn diagrams in this question. Suppose A and B are sets. (a) Use the definition of equality of sets to prove that A – B = AN B. (b) Use either the definition or set identities to prove that AN (B – A) = 0.
Question 9 f) Let A, B and C be sets. Prove that A ⊆ C and B ⊆ C, then A ∪ B ⊆ C
6. The following statements about sets are false. For each statement, give an example, i.e., a choice of sets, for which the statement is false. Such examples are called counterexamples. They are examples that are counter to, i.e., contrary to, the assertion. (a) AUBCAn B for all A, B. (b) ANØ: = A for all A. (c) AN (BUC) = (A ^ B) UC for all A, B, C.
Question 2 Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {a, d, f, g}, B = {a, c, f, i}, and C {a, g, h, i} List the elements of the set (An B) UC > Next Question
please answer the question/exercise
Prove that for sets A and B, AUB= An B. This is one of the De Morgan's laws for sets.
This is Set Theory

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Problem 3: Prove or disprove (you may use all of our set properties here, such as those from the Section 6.2 theorems): Given a universal set U , for all sets A, B, C CU, AU (B – C) = (AU B) – (AUC).