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

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

Q: Let 4, B, and C be sets. Show that a) (A - B) – CSA C. b) (A - C) n (C- B) = 0.

A: Answer

Q: , B, and C which satis

A: Given as, A= {1, |B|, |C|} B= {2,| A|, |C|} C= {1, 2, |A|, |B|}

Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

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

A:

Q: Show that if A and B are sets with AS B, then a) A UB-B. b) ANB-A.

A: Let A and B are two sets with A⊆B a) Let x∈A∪B which implies that x∈A or x∈B. Hence we can imply…

Q: What is the intersection of sets A and B?

A: The intersection of sets is a set which include the common of the two sets A and B. It is…

Q: . Let A and B be two connected subset

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let A, B, and C be non-empty sets. Then Cx BxA=C×A×B if and only if O A=B O A=B=C O None of these O…

A: We can tackle this problem easily by assuming some examples  case (i) Let A=B=C = {1,2} we have,…

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: If A,B and C are sets, then A x (B-C) = (A × B)- (A x C). |

A:

Q: If A and B are sets; A and B denote the complements of the sets A and B, then set (A- B)U(B –…

A: Using venn diagram we solve this question.

Q: Show that if A, B, and C are sets, then|A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| +…

A:

Q: if A and B are sets, then A x B=B x A

A:

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

A: A, B, C are three non empty sets,  And, it is given that A × B × C = A × C × B

Q: Let A and B be sets. Then B (B – A) is equal to the above A N B

A: The Venn diagram for 2 sets can be drawn as follows.

Q: The empty set o is open set

A:

Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

A:

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

A: A, B, C are any set, we need to show that (A-B) - C = (A-B) - (A-C) this can be done using the…

Q: If A and B are sets, then A n (B – A) = Ø. %3D

A:

Q: If A, B, and C are sets such that A ∩ B ≠ Ø and B ∩ C ≠ Ø, then A ∩ C ≠ Ø

A:

Q: Find sets A, B and C such that A ∩ B,    B ∩ C and A ∩ C are non-emptysets and A ∩ B ∩ C = φ.

A:

Q: Find the intersection of the sets. {a, b, c, d}∩∅

A: Given sets are {a, b, c, d} and an empty set ϕ

Q: If A, B, C are sets, show that a) A x B= 0 ⇒ A=0 or B = 0. b) (AUB) x C = (AXC) U (BxX C). c) (An B)…

A:

Q: Show that if A and B are sets with A ⊆ B, then a) A ∪ B = B. b) A ∩ B = A.

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: The set {(a,b) : a EA and b EB} denoted by ...............

A:

Q: Given two sets: A = {a, b} B = {b, c, d} Construct the disjoint union of A and B.

A: Procedure to find disjoint union of family of sets. Consider family of set is  Ai:i∈ℕ∪0 . Let A=⊔Ai…

Q: Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

A: No, it is not true. EXAMPLE- Let A= {2}  B= {{2},3,4} C={{2},3,4,5,6} We can see here that,

Q: For all sets A and B, ifA-B=0, then A = B.

A: For all sets A and B, if A-B=∅, then A=B.

Q: Let A, B and C be non-empty sets and let X= (A-B)-C and Y=(A-C)-(B-C) .Check whether X=Y or not.

A:

Q: b) B = {(x, y) : x² < e*+3y < 5y + 4x},

A: The objective is to find the closure of the given set.

Q: 2. Determine if the following statements are true or false. Here A represents any set. (a) ¢ C A (b)…

A: Used simple logic to prove.

Q: Let 4, B, and C be sets. Show that а) (А — В) — С сA-C. b) (А — С) n (С- В) 3D0.

A:

Q: Let A, B, C, D be sets. If A\ B CC\D, then ANDC B.

A:

Q: Let A, B, and C be three sets. If A⊕C=B⊕C, show that A=B

A: Solution : Given that A,B and C are three sets. And the Direct sum of set A and C is equals to…

Q: The intersection of sets A and B is denoted by which of the following?(a) A ∩ B (b) A ∪ B (c) A ⊆ B…

A: Sets are represented as the collection of different objects . There can be a finite set or an…

Q: Let A, B, and C be non-empty sets. Then AXBXC=A×C×B if and only if * O None of these O A=C O B=C O…

A: B=C

Q: For any sets A and B, show thatP ( A ∩ B ) = P ( A ) ∩ P ( B ).

A:

Q: Find the set P([a, b]) x P({0,1)).

A:

Q: Let A and B be sets. Prove that PLA) O P(B) = P(AO B

A: Introduction: The union of any two or more sets yields a fully new set that comprises a mixture of…

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A:

Q: Is the set {A, T,1} complete? Support your answer.

A: For a set of operators to be functionally complete, the set can be used to express all possible…

Q: Let A, B, C be sets. Simplify (A∪(B∩C))∪((Bc ∩Cc)∪C)c

A:

Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A…

A: Solution is given below:

Q: Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)are in A × B, find…

A: In AxB the first element will be from A and the second element will be from B So, x,y,z are in A And…

Q: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

A: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

Q: If A,B and C are sets, then A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

A:

Q: Let A and B be sets. Then B - (B - A) ANB is equal to the above Ā NB is equal to the above

A: Here ,we are given that A and B are two sets. We need to find  B-(B-A) : Now, Here ( B-A) represents…

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”.