For any sets A, B,C prove that if BCC then A – (BUC) = A – C. -

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

A:

Q: d) Give a recursive definition of the sequence {a„}, n = 1, 2, 3... %3D n if a,= 2 + 1; and a15 e)…

A: d)  Here, given that an=2+1=3 So, for all n, an=3 which is the recursive definition.

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

A:

Q: Let A, B, and C be sets. Prove (AUB)NC= (ANC) U(BNC)

A:

Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

Q: In cartesian product, prove that (A-B)XC=(AXC)-(BXC) A,B,C are sets

A:

Q: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

A: Solution:-

Q: 3. Which of the following statements are true? There may be more than one correct answer. A. Ø CA B.…

A:

Q: True or false. The set S-{(-1,5), (3.–15)} spans R. false a) b) true O TRUE O FALSE Drouiour

A:

Q: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: Prove that for all sets A and B, A – B = AN B

A:

Q: For all sets A, B,C.Then: (AUB) – (C – A) = AU(B The following algebraic proof is almost finished.…

A: For all sets A,B,C We prove that A∪B-C-A=A∪B-C PROOF: L.H.S:  A∪B-C-A=A∪B-C∩ACby Complement Law(we…

Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

A:

Q: Let A:= {2} and B:= {2,3,5}. Give the Cartesian product of sets A and B, furthermore the power set P…

A:

Q: For all sets A, B, and C, prove that (AUB) - (CA) = AU (B-C) Please indicate the reason for each of…

A:

Q: (19) Prove or disprove ∀ sets A, B, and C: (A – B) − C = (A – C) – (B – C).

A: We will use the Venn diagram show the proof: Left side:

Q: 2. Prove for any sets A, B that (An B) = A if and only if A C B.

A:

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Suppose A, B, C are sets. Prove that (AUB) – C = (A − C) U (B − C)

A: A∪B-C=A-C∪B-C

Q: (ANB) –C= (A –C)NB.

A:

Q: Prove: For all sets A, B and C, An (B-C) = (ANB) - (ANC).

A:

Q: The set {[1 2 0 1, [2 0 4 1, [O 4 5 ]}spans R3 صواب İhi

A:

Q: Q13: Prove or disprove the following: (AUB) - C = (AUC) - (BUC) where A; B; and C are sets.

A: Q13.   The given statement is false.  Counterexample :    Consider   A = { 1, 2, 3 }…

Q: The solution to the initial value problem of a second order ODE y" + by' + cy = et can always be…

A:

Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B)n (A × C)

A:

Q: Let A, B, C be sets. Prove A U (B and C) = (AUB) and (AUC)

A:

Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B

Q: 11. For sets A and B, define AAB=(A\B) U (B\A). (a) Let A and B be sets. Prove that A = B if and…

A: For sets  A and B , define                             A∆B=(A \ B)∪(B \ A) .  Then we have to show…

Q: Let A, B, and C be sets. Prove or disprove: A × (BnC) = (A × B)N (A x C).

A:

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

A: