Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. Does the equality |A u B|=|A|+|B| hold for every set A ??? B Is it true that (A−B)−C=A−(B−C) for some sets A, B and C

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First we write U and the set in roaster form.

Q: (d) D= {n €Z:n −3} (e) E = {}\{}

A: Here we have to find the set D and E in list form.

Q: A W C с 3 р a 6.0 D g h f B

A:

Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

A:

Q: -4 A = -3 6. -8 b3 5.

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Q: Use an algebraic proof to show that for all sets X ,Y and Z : (X – Y)n ZC = x – (Y u Z) Do not…

A:

Q: Prove or give a counter example, let A and B be sets. Then P(A∪B) = P(A)∪P(B)

A:

Q: For Exercise, write the set as a single interval. [(-0, 6) U (10, o)] N [8, 12)

A: We will draw them on a number line. Draw:

Q: Express the set in roster form. B = (x | XEN and x is a multiple of 7)

A: For given set B we have to write it in roster form.

Q: Use the given sets to find |X n Y. U = х, у, Y = {suav.e}

A:

Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: Give an example of two sets that meet the following condition. If the condition is impossible to…

A:

Q: Q17D. Define the sets A, B, C, and D as shown. Find (A ∩ C) ∪ (B ∩ D).

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 9}.  (Enter your answers as a…

A:

Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

Q: Write ALWAYS if the statement is always true, SOMETIMES if it is sometimes true, somet false, and…

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 5}.  (Enter your answers as a…

A:

Q: State whether each of the following statement is true or false. Justify your answer.(i) { 2, 3, 4, 5…

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

A: We Know that,  If U is a universal set and A be any subset of U then the complement of A is the set…

Q: Let A and B be two sets. We denote A- B = { x | x∊A and xÏB}. Prove that A∪B=(A−B)∪(A∩B)∪(B−A).

A:

Q: Assignment Instructions: Answer the following questions. Remember to show all relevant work and…

A: Here given:- A,B,C are sets For any two sets S1 and S2 S1∪S2=S1+S2-S1∩S2   A∪B∪C=A∪B+C-A∩B∪C…

Q: True or False?

A:

Q: Prove or disprove: If A, B, and C are sets, then A × (B − C) = (A × B) – (A × C).

A:

Q: Prove or disprove: For all sets A,B and C: (A-B)-C = A-(BUC).

A:

Q: Determine if each statement is true or false. 1. If A not equal to B then A ∩ B = empty set. 2. If…

A: we will be using basic set theory to answer these questions

Q: Let A and B be sets. Prove that A Ū B = (A − B) U (B − A) U (ANB).

A: Let A and B be any two sets.Prove that: .

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

A:

Q: (20 pts) Answer the following questions about the set A = {3,Ø, {T, e}}: a. What is JA|? b. Is n E…

A: With the help of concept of set theory and Cartesian product we can solve all these questions-

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Let A, B and C be sets. Use the algebra of sets to verify each statement. 1. A- (B U C) = (A – B) n…

A: Solution

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

A:

Q: The following statement is false: If A₁ A₂ A3 = Ø, then |A₁ U A2 U A3| = |A1| + |A2| + |A3|. Provide…

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.