Let A, B and C be any three sets. Then Ax (BUC)=

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

A:

Q: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

Q: Let set A be the set of face cards and B be the set of all spades in a regular deck of cards. State…

A: There are 12 face cards in a regular deck of cards and 13 spades in a regular deck of cards. Set A:…

Q: TION 4 If A, B, C be three sets such that Au B = AUC and ANB = ANC, then : O B = C O A = C O A = B =…

A:

Q: Let S = (x: (x - 1)² = 0}, state where S is singleton set or not.

A:

Q: Express (4, 10) as a set {x : |x – al < c} for suitable a and c.

A:

Q: (4.2) For sets A, B and C, prove that (An B) x C = (A x C) n(B x C).

A: Here we have to prove that (A∩B)×C=(A×C)∩(B×C)

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: If either A or B empty set then Ax B equal empty O A

A: The solution is given as

Q: Let A, B and C are be sets. Show that we can have AnB= AnC without B=C

A:

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

A:

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

A: Let A, B and C are sets. We have to find out that A-B = A- C implies B = C or not If not then we…

Q: Suppose A and B are two sets such that ANB = Ø. Which of the following statements is/are true? (i)…

A:

Q: Suppose that A, B, and C are sets such that A ⊕ C = B ⊕ C. Must it be the case that A = B?

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Q: 4. Let A and B be sets, prove that P(A)UP(B) C P(AUB).

A:

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

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: Express (4, 10) as a set {x : |x − a| &lt; c} for suitable a and c

A: Write the given interval in inequality form as follows: 4&lt;x&lt;10

Q: The intersection of sets K and L will

A: our objective is to find the intersection

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

A:

Q: For any two sets A and B, if m* (A) = 0, then m* (AUB) = m* (B). In particular, if BCA, then m* (B)…

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Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: or any of the sets id, bic it a,bsCthen a b anteo

A:

Q: Assume that the statement applies to all sets. Is it true or false? A – (BO C) = (A – B) (A – C) 2.

A: A-(B INTERSECTION) C= (A-B)INTERSECTION(A-C)

Q: Let A, B, and C are three sets, prove that Bx(AUC)=(B× A)U(B×C)

A: "Since you have posted multiple questions, we will answer the first question. If you want the…

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: Determine whether or not the following is true: for all sets A, B and C, (AUB) (C\A) = AU (B\C); If…

A:

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

A:

Q: Give a counterexample to show that the statement For all sets A, B and C, if A⊈BandB⊈C,thenA⊈C.…

A:

Q: What is the complement of the set X? How is it denoted?

A: Universal set is always given to find complement of a set. Complement of a set 'X': It includes…

Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

A:

Q: Give an example of sets S and T where P(SUT)メP(S) U P(T)

A: Let, S={3,7} and T={4} be any set and P(SUT) be a power set of union of S and…

Q: Let A B be any Sets then A B ifp PA) e PCB)

A:

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

Q: Let A, B, and C be sets. Does A – C = B – C imply A = B? If so, prove it. If not, give a…

A: We have to give a counter example for  A – C = B – C imply A = B.

Q: Express (4, 10) as a set {x: Ix - al&lt; c} for suitable a and c.

A:

Q: {(x,a), (x,b), (x,c), (y,a), (y,b),(y,c)} is the Cartesian product AXB of two sets given as

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: Let A, B, C be three sets. Show that if B C A and C C A \ B, then BC A \C.

A: Given: Let A, B, C be three sets. To show: If B⊆A and C⊆A \ B, then B⊆A \ C.

Q: For any two sets A and B, if A=B,then A=B صواب ihi

A: Given a statement

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

A:

Q: Prove that if A ~ B then P(A) ~ P(B).

A: Consider the provided question,

Q: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: Let A and B be sets. Then B (B – A) -

A: Complement of set A =1-A

Q: Let A and B be finite sets with |A|=10, |B|=5, |A∪B|=12 what is |A∩B|?

A: Given,  |A|=10 |B|=5 |A∪B|=12 |A∩B|=?

Q: what does R mean in R-C=C' , is that a universal set ?

A: Here R=universal set.   The Venn diagram of C is:   The Venn diagram of R - C is:

Q: If Q, R, S are sets then QU(ROS) and (S-(QUR)) U (R- (QUS))) are disjoint sets.

A: This is a problem of the set theory. Two sets QU(R∩S) and ((S-(QUR))U(R-(QUS))) are given. The…

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”.