4. Suppose you wanted ; –) and :0 to be the elements of a set S. (a) How could you indicate this? In particular, how would you convey to someone else that the elements of S are ; -) and :0, and not some other elements? (b) Describe in words how you would indicate the elements of a set.

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

A:

Q: Let S be a set with |S|=6 . In how many ways can we partition the set S into three non-empty parts?

A: Answer:   3   Here    |S| = 6 So there are total 11 possible partitions which are 6 5+1 4+2 3+3…

Q: 2. Classify each set as closed, open, or neither. Justify your answer. A= {-+:nEN} E. 1-:] [0, 1)

A:

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.

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

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its (b) a set…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Prove or disprove: For all sets A and B, An(AUB)

A: We have to prove or disprove , for all sets A and B A∩(A∪B)=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: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

A:

Q: How many proper subsets does the set T={h,f,k} have

A: A set is given by, T = h, f, k. The objective is to find the number of proper subsets the T have.

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: Let S be a set containing 700 elements. which is greater, the number of subsets of S having 400…

A: Let S be a set containing 700 elements. We have to justify, Which is greater, the number of subsets…

Q: 2. (i) Show that given finitely many countable sets A1, A2, , An, the set A1 x A2 x .. x An is also…

A:

Q: 2. Specify the set B in set-builder form by giving a written description of its elements, where B =…

A:

Q: A survey of 500 farmers showed that of the​ farmers, 26 grew only​ wheat, 114 grew only​ corn, 93…

A: The following situation can be represented by venn diagram given below: Rectangle(universal set)…

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

A:

Q: 6. Let S be a set containing 700 elements. which is greater, the number of subsets of S having 400…

A: We have given as set 'S' with '700' elements in it. Concept:  CARDINALITY -- Cardinality is the…

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A:

Q: Use the method of intersection of sets to compute the following. (a) GCD(12,16,8) and LCM(12,16,8)…

A:

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

A:

Q: _1. It is a pictorial representation of the relationships between sets wherein the sets are…

A: Since you have posted multiple questions. We will solve first question. If you want the other…

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

A:

Q: Suppose S is a set having n elements and T is a set having m elements. Which of the following claim…

A: Suppose S is set having n elements and T is a set having m elements. That is n>m More precisely,…

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

A: Topic:- ven diagram

Q: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

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: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

A:

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

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Q: (3) Let S = {; Find with prove :m eN,n E N}. %3D suprenum of S. (4) What is an unbounded set?

A:

Q: 2. Specify the set B in set-builder form by giving a written description of its elements, where…

A:

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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

A:

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

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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…

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Q: 3. Assume there is binary operation o that is defined for a set T which consist of two elements.…

A:

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

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

A:

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

A:

Q: 2. Prove that by laws of set, (A - B)- (B - C) = A -B

A:

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: 5. Consider the generic Venn diagram for three sets. (a) Add one figure showing a fourth set D. (b)…

A: The generic Venn diagram is: