Use Venn diagrams to show for sets A, B, and C:     a. ( A ∪ B ) ⊆ ( A ∪ B ∪ C ) b. ( A ∩ B ∩ C ) ⊆ ( A ∩ B ) c. ( A − B ) − C ⊆ A − C

Q: Use a direct proof technique to prove the following theorems:   For all integers x and y, x2 + y2 −…

A:

Q: Explain what is wrong with the following proposed definition of the set membershippredicate ∈ :∀ x,…

A: Introduction :

Q: 2) f is a 3-to-1 correspondence from the domain A to a target set B. Given this information, which…

A: Given that, f is a 3-to-1 correspondence from the domain A to a target set B. That means A and B are…

Q: The set operations union and intersection are commutative.a. E1 ∪ E2 ≡ E2 ∪ E1b. E1 ∩ E2 ≡ E2 ∩…

A: The FIrst question will be answered only. a. To prove: E1 ∪ E2 ≡ E2 ∪ E1 Let us consider,  x∈ E1 ∪…

Q: s A ⊆ B if  A = {8, 10, 12, 14}  and  B = {8, 10, 12, 16, 20}?

A: Here,  The elements of set A are { 8, 10, 12, 14 } And the elements of set B are { 8, 10, 12, 16, 20…

Q: 5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which…

A: Regression Regression is a statistical technique used in finance, investing, and other fields that…

Q: QUESTION 3 Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is 'wise", R(x): "x is…

A: The solution for the above given question is given below:

Q: what is independent sets ? what is maximal independent set ? what is the independence number? what…

A: A set of vertices I is called independent set or a stable set, if no two vertices in set I are…

Q: De Morgan’s laws also apply to sets.   De Morgan’s laws   (A U B)’ =  A’ ∩ B’ (A ∩ B)’ =  A’ U…

A: Given equation to prove:A – (A – B) = A ∩ BGiven De Morgan’s laws(A U B)’ =  A’ ∩ B’(A ∩ B)’ =  A’ U…

Q: Given A and B are sets, prove that (A ⋃ B) ⋃ C = A ⋃ (B ⋃ C) by showing (A ⋃ B) ⋃ C ⊆ A ⋃ (B ⋃ C)…

A: We are going to prove associative property in sets which is : (A ⋃ B) ⋃ C = A ⋃ (B ⋃ C). Please…

Q: Show that if A ⊆ C and B ⊆ D, then A × B ⊆ C × D

A: Here is the explanation regarding the proof.

Q: Let X = {l ∈ Z | l = 5a + 2 for some integer a}, Y = {m ∈ Z | m = 4b + 3 for some integer b}, and Z…

A: Given, X = {l ∈ Z | l = 5a + 2  Y = {m ∈ Z | m = 4b + 3 Z = {n ∈ Z | n = 4c − 1 To Prove: Y ⊆ Z

Q: (a) Is 2 ⊆ {2, 4, 6}? (b) Is {3} ∈ {1, 3, 5}?

A: The symbol ∈ indicates set membership and means “is an element of” so that the statement x∈A means…

Q: Let A = {p, q, r, s} B = {r, t, v} C = {p, s, t, u} be subsets of S = {p, q, r, s, t, u, v, w}.…

A: The solution is given below for the above given question:

Q: A) Prove that if A ⊆ B and B ⊆ C, then A ⊆ C. B) Prove that if (A − B) ∪ (B − A) = A ∪ B, then A ∩…

A: A. Prove that if A ⊆ B and B ⊆ C, then A ⊆ C. To prove that A ⊆ C, we need to show that every…

Q: Write proof to the following statements. (a) Given that (A ∪ B) ∩ B′ ⊆ C prove that 2A∩B′ ⊆ 2C .…

A: What is set: A set is a collection of distinct objects, considered as an object in its own right.…

Q: Write proof to the following statements. (a) Given that (A ∪ B) ∩ B′ ⊆ C prove that 2A∩B′ ⊆ 2C .…

A: (a) Given that (A ∪ B) ∩ B′ ⊆ C, we want to prove that 2A∩B′ ⊆ 2C, where 2A denotes the power set of…

Q: Computer Science Is it true that A ∩ (B ∪ C) ∩ D = (A ∩ B) ∪ (C ∩ D) for all sets A, B, C and D?…

A: Solution for given,  Is it true that A ∩ (B ∪ C) ∩ D = (A ∩ B) ∪ (C ∩ D) for all sets A, B, C and D?…

Q: Given sets A and B, to prove that (A − B) ∪ (A ∩ B) ⊆ A, we suppose that x ∈ ______ and we must show…

A: Answer is given below

Q: Let A = {1, 2, 3},         B = {{1}, 2, {1, 3}},         C = {1, {1}, 3}.   Compute the following…

A: Compute of given sets

Q: Create a Venn diagram for each of the sets below. 1.  (A ∩ B ∩ C) 2. (A∪B) ∩ C

A:

Q: Show that if A and B are sets with A ⊆ B then A ∪ B = B.  (Hint: Show that x ∈ A ∪ B implies x ∈ B…

A: Given that A ⊆B Let x ∈ A U B which means that x ∈ A or x ∈B. Therefore we can  say that: A U B ⊆ B…

Q: Show that (A − B)∪ [(B − A) ∪ (A ∩ B)] = A ∪ B using set identities. Give reason at each step.

A: (A − B)∪ [(B − A) ∪ (A ∩ B)] = A ∪ B A − B = {x, x ∈ A ∧ x 6∈ B}. Then A ∩ B¯ = {x, x ∈A ∧ x ∈ B¯},…

Q: The format P(X) represents as a power set of given "X", (of all X's subsets)   Now, assume there…

A: Your answer is given below.

Predicates

A predicate is a function defined with set of variables, which returns the result True or False. The output of a predicate is a Boolean value as a response when given a set of parameters: