1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a counterexample.

Q: Let A and B be two sets. Determine which of the following statements are true and which are false.…

A:

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: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Let A, B, and C be sets. Show that (A − B) − C = (A − C) − (B − C).

A:

Q: 1. Let A, B, and C be sets. Given A C B, show that (a) AnC C BnC. (b) ВС А.

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: Y={a,b,c,d,f} Is the following statement True? ∅⊆Y

A: The given set is                        Y={ a , b , c , d , f } We know that for every set S , S⊂S ,…

Q: 5. Consider the following statement: For all sets A, B, and C, then AU (BNC) = (AUB) nC. Either…

A: Let value of set A,set B and set C are respectively. A={1,2,3,6,7} B={3,7,8,9} C={2,3,6,9}

Q: Let A, B, C, and D be sets.

A: First, (AxC)U(BXD) ⸦(AUC) x(BUD)Take left hand side first , let  (x,y) ∈(AxC) U(BxD)=> (x,y)…

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: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: 1. If={1,2,3,4,5) and = (0, 0, (5), (1,2), (1,5), (3,4), (1,2,5), (2,3,4), (3,4,5), (1,2,3,4]} then…

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: If={1,2,3,4,5) and = (0,0, (1), (2,3), (4,5), (1,2,3), (1,4,5), (2,3,4,5)} then If Q=set of positive…

A:

Q: 3. Let A, B, C be sets. Provide a proof or a counterexample for each of the following statements. a.…

A:

Q: Let A, B and C be sets. Consider the following statements. Which of them are true? 1. Ax B = B×A 2.…

A: Given that A, B and C are sets. Note: According to Bartleby guidelines we can solve only first three…

Q: prove the following statement If A, B, and C are sets, then A - (BnC) = (A - B) U (A - C). Suppose…

A: Since you have posted a question with multiple sub ports, we will provide the solution only to the…

Q: Let A and B be sets. The symmetric difference of A and B, denoted A∆B, is the set A∆B = (A −B) ∪(B…

A:

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: Let A, B and D be sets. If A n B = Ø then prove that (A – B) – (B n D) = A.

A: Take x in left hand side and prove it belong to A and vice versa.

Q: Solve the following system. 3x+9y+25z=-2 -2x-7y-19z=1 3x+9y+24z=-3

A:

Q: 3. Let A, B, C, and D be sets. (a) Prove that (A × C) n (B × D) = (An B) × (Cn D).

A: Let A, B, C, and D be sets.To prove the equality, we have to show that, LHS is a subset of RHS and…

Q: 1. Use set identities to show that (A U B) n (B U A) = A where A and B are sets. Let A = {1,2, 3}…

A:

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: If A,B and C are sets, then (AUB)-C=(A-C)U(B–C).

A: