5. Prove, if true, that if A, B and C are sets that A - (Bn C) = (A - B) U (A - C). If it is not true, give a counterexample. Determine by fiddling around with examples, whether it is true. If that is what you believe, it is a simple set-theoretic proof.

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: Let A,B,C,D be set. Prove that (A x B) \ (C x D) = [(A\C) x B] or [A x (B\D)] Kindly Indicate the…

A:

Q: For any sets A, B, and C, A \ (BUC) = (A\ B) U (A\ C). For any sets A, B,C, if AN B C C, then (A \…

A:

Q: For two sets A and B, if A=B, then (i) A and B have the same elements (ii) ACB and BCA (iii) x €…

A: Here we have to find the properties of two sets A and B is A= B.

Q: Which of the following is the correct representation of A {2,4,8,16,32,... } in set builder…

A: To determine the correct representation of A=2, 4, 8, 16, 32, ... in set builder notation.

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: When is a set compact?

A:

Q: (1) Prove, or come up with as simple a counterexample as you can: For sets A, B, in the context of a…

A:

Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

A:

Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

A:

Q: le Let A, B, C be sets. By drawing Venn diagrams, determine if the following statements are true or…

A:

Q: Prove or disprove: Suppose C and D are sets with C ∩ D = ∅. Then P(C) ∩ P(D) = ∅.

A:

Q: Assume that the universal set is Z. Consider the following sentence: (3t = Z) (t •x = 20). (a)…

A: Here, in the question, it says, such that tx= 20.We know a statement in logic and mathematics is a…

Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

A:

Q: If A and B are two sets prove that AUB=AUB

A: To prove that A complement union B complement is equal to the complement of the union of A and B .…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

A:

Q: (1) If A is an uncountable (2) Z† × Z is a countable set. Select one of the following choices: set…

A: A countable set is a set that can be put into one-to-one correspondence with the natural numbers…

Q: Prove by giving an example that if any set A, g. l. b(-A) = - l. u. b(A

A: Take a set A with two elements 1 and -1

Q: Determine the truth or falsity of the following statement: “It is possible for sets A and B to have…

A: Given data: The two sets A and B are considered. The difference of two sets A and B (A - B) can be…

Q: Let A, B, C, and D be four sets. Prove the following two statements. a. Suppose that An BCC\D. Prove…

A: Statement aSuppose that A∩B⊆C∖D. Prove that if x∈A and x∈D, then x∈/B.Proof:1. Let x∈A and x∈D.2.…

Q: Let A and B be sets. Prove that Ac B if and only if AnB = A.

A:

Q: b) By using the laws of set theory, show that [(A U B) n (An C)] u (B n C) = A U B.

A: Here we have to prove left hand side is equivalent to right hand side using laws of set theory

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: (b) If BC A, then ACB. (Recall that A represents the complement of set A.)

A:

Q: 3. Give an example of sets A and B and a universal set U such that A c B. Find A and B.

A:

Q: 5. Let A, B, and C be sets. Prove or disprove that if AUB ANC, then A & C or BJA.

A: We disprove the statment with suitable example

Q: 4. Let A and B be sets in a universe U. Consider the following two statements: i. P(AU B) ii. P(An…

A:

Q: A, B are sets. Show that (AUB) = An B. Hint: use t proof by containment method.

A: A, B are sets .We need to show

Q: Let A, B and C all be sets with a universal set U. Prove or disprove the following statements: i. If…

A: Let's prove or disprove each statement:i. If B⊆C then (A×B)⊆(A×C):Proof:Assume B⊆C. Let (x,y) be an…

Q: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

A: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

Q: Suppose that A and B are finite sets. Prove that AxB is finite.

A: Result 1 :  A be an non-empty finite set if and only if cardinality of A is a finite natural number…