10 b)  Let A, B, C and D be sets. Prove that C ⊆ A and D ⊆ B, then C ∪ D ⊆ A ∪ B

Q: Provide a counterexample for the statement: For any sets A,B and C, А - (В -С) — (А - В) — С.

A:

Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

Q: If a set A has 63 proper subsets, what is |Al? 6. 7 8. 9

A:

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: (1) *, Let A and B be sets prove the following. (c) A C B if and only if B° C A°.

A: Let A and B be sets.

Q: Let A, B, C be sets. Prove (AAB) -C = (A- (BUC))U(AN BnC)

A:

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

Q: 2. Suppose A, B, and C are sets. Prove that (AUB) \C CAU (B \ C).

A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

Q: 3. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

A:

Q: Let S be the universal set, where: S = {1, 2, 3, .., 23, 24, 25} >....

A: Given…

Q: Suppose that A and B are sets. Prove that A- B = AnB.

A: Suppose that A and B are set. Prove that A-B=A∩B¯.

Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: Suppore that A and B aru Awre set such that (AI= IB1 Show that %3D (P(A), P(B) denote the pouser…

A: We used the concept that if a set contains n elements then it power set contains 2n elements .

Q: How would a mathematician say: “Take the set {s,u} and give it the name G” Let D = {u,j}. Is j a…

A: 1. Let, G=s,u 2. Consider a set D=u,j. A set X is a subset of another set Y. If all the elements of…

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: 11. Use set identities or different proof method to show that: a) (B- A)U(C- A) = (BUC)- A b) (4 –…

A:

Q: 6. Let A, B be finite sets. Show that if JA\ B| = |B\ AJ, then |A| = |B|.

A: The order of a set defines the number of elements of the set. For two finite sets A and B,…

Q: 10. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: Let C and D are be the subsets of some universal set U. Then D-C = C'nD is

A: We have to identify the statements as true or false.

Q: Prove that if A1, A2, ..., A, are any n > 2 sets, then A NA2 N …… A„ = A¡ UA2 U.…UA..

A: We will  prove the given statement using mathematical induction method.

Q: Let A, B and C be sets. Use an element argument to prove that (A - B) - C≤A-C.

A:

Q: (4) Prove by contradiction, for any sets A and B, if ACA- B, then An B= Ø

A:

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

A:

Q: 19. If A={People who live in Colorado} B={People who live in Denver}, draw a Venn diagram relating…

A:

Q: 2) Explain how you count the number of elements in the set A = {n EN| n <500 and gcd (n, M) = 1},…

A:

Q: Let the Universal Set, S, have 78 elements. A and Bare subsets of S. Set A contains 44 elements and…

A: Given data: The numbers of elements in the universal set are n(S)=78. The numbers of elements in the…

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

A: This question is related to Set theory, We will solve it using given information.

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

A: Given that A, B and C are three sets. We need to find A×{B ∪ C}.

Q: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: 20. What is the cardinality of each of these sets? а) и c) {Ø, {Ø}} b) {Ø} d) {Ø, {Ø}, {Ø, {Ø}}}

A:

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Let A be the set of students in your discrete math class and B is the set of students at Arizona…

A: A) A is the set of students in the discrete math class. B is the set of students at Arizona majoring…

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

A: Given 3 sets A, B and C. We have to prove that B×A∩C=B×A∩B×C. For this, we have to show that…

Q: Are there sets A and B such that |A|=|B|,|A|=|B|, |A∪B|=10,|A∪B|=10, and |A∩B|=5?|A∩B|=5? Explain.

A: Given:A|=|B|, |A∪B|=10, and |A∩B|=5The Venn diagram is

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

Q: The Venn diagram shows sets A, B, C, and the universal set U.

A: Given Venn diagram:

Q: 1. If A ana B are sets, show that Ac B if and only if An B = A.

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

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, and C be sets. Prove that if A CB and B C C, then A C C.

A: Let, x belongs to A. Since, A is a subset of B, so, x belongs to A implies that, x belongs to B. So,…

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

A:

Q: 2. Draw a Venn diagram for the set AU(BnC).

A: We first draw U, A, B, C

Q: Show that if A and B sets then A – B = ANB

A:

Q: If sets X and Y are uncountable, then prove or disprove that X-Y is uncountable.

A: Here we will prove or disprove the given statement.

Q: b) Prove the second De Morgan law in by showing that if A and B are sets, then AUB=ANB i) by showing…

A:

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

A:

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…

Q: Let the Universal Set, S, have 120 elements. A and B are subsets of S. Set A contains 92 elements…

A: Universal set s=120 elementsSet A=92Set =27elemants in  A and B=21

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”.