Let A and B be finite sets. (a) Explain why n(ANB) s n(A). (b) Explain why n(A) s n(AUB). (c) Suppose n(ANB) = n(AUB). What more can be said about A and B?

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

A:

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: What is a set?

A: Definition of the set:

Q: The set of elements that are members of set A or set B or of both sets is called the --------------…

A: The union of two sets is composed of elements of the same two sets.

Q: Give an example of each of the statements below using the sets indicated (and power sets) to show…

A:

Q: The set of elements common to both set A and set B is called ----------------- the of sets A and B,…

A: Sets are basically a collection of well defined and distinct objects. These objects can be anything,…

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 =…

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Q: What is meant by Intersection of sets?

A: Let A and B be the two sets. Then the set of all common elements of A and B is called the…

Q: Using contradiction method, prove that for every nonempty sets A and B, An (B- A)=0.

A: The given problem is to prove the following set identity using the contradiction method.

Q: 26

A: The objective is to find an infinite collection of closed sets whose union is not closed.

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

A:

Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: 4. True or False. Determine whether the given pairs of sets are equal. a. A = {2n + 1|n e W} ; B =…

A: We will write the given sets in roster form then by comparing both sets we will determine if they…

Q: Express the following in set-builder notation: (c) The open interval C = (−2, 2). (d) The set D of…

A: (c) C = (-2, 2) = { x ∈ R :  - 2 < x < 2 } (d) D = { A ⊆ N : #(A) = 20 } Where, #(A)…

Q: (a) Prove the following statement using the element method for proving that a set equals the empty…

A: (a) Suppose that A and B are two sets. It is known that, B-A represents the set of elements in B…

Q: Explain and give a simple example that shows that the intersection operation on sets is symmetrical.

A: Answer

Q: For the set {a,b,c,d}, list  a) all the arrangements of 2 objects.  b) all the subsets of 2…

A: Given problem Given that   For the set { a, b, c, d }, list  a) all the arrangements of 2 objects…

Q: Let X be the set comprising all numbers of the following two types: • Natural numbers; • Natural…

A: From (i) & (ii), we conclude that the function f is well defined.

Q: Using the fact that "a countable union of countable sets is countable", show that the statement that…

A: Please see the below picture for detailed solution.

Q: (iii) ((A – B)UC – D) specified using set builder notation without any word -

A:

Q: Let A, B, and C be finite sets, with ACBC C and n(B) = 7. (a) What are the possible values of n(A)?…

A: Given:  A, B, and C are finite sets. A ⊂ B ⊆ C and n(B) = 7. Subset and subset notations: A subset…

Q: Prove using the properties of set operations: a. ((AUB)–C)° = (A–C) – (B – C)

A: Solution

Q: b. Define the finite and infinite sets in your own words and give example for each set.

A: We use the definition of finite and infinite set to answer the given question.

Q: Explain the difference between set A and set B

A:

Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

Q: Using equality of sets, prove that (?∩?)′ = ?′ ∪?′

A:

Q: Answer the remaining questions about set theory and probability theory.   d) Give an informal…

A: Given  X⊂ Y  Y⊂ X

Q: Proving a divisibility relation is transitive

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Q: let A be a set with n elements and B a set with m elements. How many different functions are there…

A: Concept introduction: Relation: A relation between two sets is a collection of ordered pairs…

Q: Use element argument method to prove that if A and B are sets such that P(A) ≤ P(B), then A ≤ B,…

A: I just used the definition  Of power set and subset of set

Q: What are the basics of a set?

A: Set:A set is a collection of well-defined distinct objects. Here the objects are known as the…

Q: Give an example that achieves the following two infinite sets A and B with A C B and A - B.

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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: Find the complement of the set given that U={x xEI and -3<x<9}. (Enter your answers as a…

A:

Q: It is the selection of objects from a set.

A: This is the problem of combinatorial. finite math, counting.

Q: What is the set R of all real numbers?

A: Real numbers are the numbers which include both rational and irrational numbers. A real number is a…

Q: Q3 In a plane of 160 passengers, the airline has provided 48 meals of chicken rice, 78 meals of…

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Q: Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).…

A:

Q: 6. Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below…

A: (i). Let  S = { ..., -5, - 4, - 3, - 2, - 1 }

Q: Q3 ( Let A, B and C be sets. Show that (C – A)n (A – B) = 0, without using membership tables.

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Q: Prove directly that the union of two disjoint sets, where one is countably infinite and the other is…

A:

Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Give an example of each of the statements below using the sets indicated (and power sets) to show…

A: (a) If A belongs to B means A is the subset of B and B is a subset of C.

Q: C. Think of a set with m + n elements as composed of two parts, one with m elements and the other…

A: m+n elements as composed of two parts.

Q: se an element of argument to prove for all sets A,B,C (A-B)∩(C-B) = (A∩C)-B please explain if…

A: Let A, B, C are the three sets which can be assumed as,  A=1, 2, 3, 4 B=3, 4, 5, 6 C=1, 2, 3, 7, 8…

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: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B ∪ C). True or False.

A:

Q: Which of the following sets is NOT well-defined?:   -The set of correct answers in the exam. -The…

A:

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”.