(2)(a) Use an element proof to prove that for any sets A, B, and C, if A C C and BCC, thenAUBCC.(b) Can you see what logical principle from chapter 2 that the above corresponds to?

a. Assume that x∈A∪B. This means that x is either in A or in B or possibly in both.Since A⊆C, if…

Answered: (2) (a) Use an element proof to prove…

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) B(x) means that " x has a car", T(x,y) means that "x and y talked on the phone", where the universe of discourse for x and y consists of all the workers in a company. Translate the following sentences into logical expressions using quantifiers? a) Everyone in the company with a car has talked on the phone with at least one other worker in the company. b) There are two workers in the company who have not talked with each other on the phone. Translate the following logical expressions into a meaningful English sentence? c) 3x Vy (x=y) v (B(x) ^ -T(x, y))) d) 3x 3y Vz ( T(x, z) →-T(y, z))
All about math
If A, B, C are sets then the law (An B) UC = (ANC) U (BNC) is a distributive law. Select one: O True O False
Consider the following two statements: EA, for all sets A. A, for all sets A. Which of the following is correct? (1) (2) Both statements are true. Statement (1) is false, and statement (2) is true. Both statements are false. Statement (1) is true, and statement (2) is false.
Let A and B be sets such that B (1) If A is finite, then B is finite. (2) If A is infinite, then B is infinite. (3) If B is finite, then A is finite. (4) If Bis infinite, then A is infinite. Which of the following is true? Statements (2) and (3) are true. Statements (2) and (4) are true. Statements (1) and (2) are true. Statements (1) and (3) are true. None of the above is correct. Statements (3) and (4) are true. Statements (1) and (4) are true. A. Consider the following statements:
Let U= {x|x is a positive integer and x <10} be the universal set, A = {x|x €U and x is a factor of 12} and B ={x |x eU and x is a multiple of 2}. Determine the elements of а) the sets A and B. For each of the following questions, give a reason to support your answer. (i) Is A-B = {1, 2, 3}? (ii) Is AcB? (iii) Is BC A? (iv) Is A = B?
c and d part solution
In this problem, you will get some practice with the logic of sets, i.e., ways of putting sets together to make other sets. The main tool here will be presence tables. Your task is to verify, using presence tables, that the following relations between sets are true.
question below
8. Let A, B and C be sets. (a) Suppose that AC B and BC C. Does this mean that A SC? Prove your answer. Hint: to prove that A CCyou must prove the implication, "for all x, if x € A then x € C." (b) Suppose that A E B and BE C. Does this mean that A € C? Give an example to prove that this does NOT always happen (and explain why your example works). You should be able to give an example where |A| = |B| = |C| = 2.
For each of the following statements, if the statement is true, then give a proof, and if the statement is false, then write out its negation and prove. (a) For all sets A, B and C, AU (BC) is a subset of (AUB) n(AUC). (b) For all sets A, B and C, (AUB) - C = (AC) U (B-C).
2. For each of the following logical equivalences state whether it is valid or invalid. If invalid then give a counterexample (e.g., based on a truth table). If valid then give an algebraic proof using logical equivalences from Tables 6, 7, and 8 from Section 1.3 of textbook. (a) p→ (q → r) = q → (-p v r) r) ^ (q → r) = ((p^q) → r) (c) (p→ q) ^ (p → r) = (p→ (q^r)) (d) ((pvq) ^ (¬p v r)) = (q v r)

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(2) (a) Use an element proof to prove that for any sets A, B, and C, if A C C and BCC, then AUBCC. (b) Can you see what logical principle from chapter 2 that the above corresponds to?