a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at your school who are not taking discrete mathematics c) the set of students at your school who either are sophomores or are taking discrete mathematics

Q: Decide with a proof that the set Nk is countable or not, where N is the set of natural numbers and k…

A: According to the given information it is required to proof that the set

Q: Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪…

A:

Q: State the formula for the Principle of Inclusion and Exclusion for 3 sets. Draw a Venn diagram…

A: The formula for The principle of inclusion and exclusion  for three sets A |A\cup B \cup C| = |A| +…

Q: Suppose that S is a non-empty finite set. Prove that ? has as many even-sized subsets as it does…

A: Let S be a non-empty set. Let A be the set of even sized subsets of S and let B be the set of odd…

Q: 1. Draw a Venn diagram showing the following: (a) Two sets A, B, where every element of B is an…

A:

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (CC n D) U (C n D) = D where Ce…

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

A:

Q: Write the following sets in roster notation:

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Q: Let *' be defined on the set N. Which of the following are both commutative and associative?

A:

Q: Set C is a set of states in the United States whose names start with the letter H in roster form

A: In this question we have to write a set C in roster form which contains states of United Stated…

Q: A group of high school students reports who has a job and who plays sports. The information is…

A: lets the event having a job = J event that random person is in sports  = S probability of having a…

Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: The solution is as shown below

Q: Draw a Venn diagram to show the set  An(B U C')

A: Furst find B U C' then An(B U C').

Q: For an element to be in the intersection of sets A and B, the element must be in set Am in set B.…

A: Any elements of A intersection B must be in set A and in set B

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

A: Note that, a set is a collection of objects. All the object that are clearly determined in a set are…

Q: Sketch the following sets and determine which are domains. * |z - 2+il 4 * Im z>1 * Im z =1 3.

A:

Q: the set of students at your school who either are not sophomores or are not taking discrete…

A: Given: Suppose that A is the set of sophomores at the school and B is the set of students in…

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

A:

Q: Construct a Venn diagram illustrating the sets below. U={1, 2, 3, 4, 5, 6, 7, 8} Y={1,4, 6}…

A: Given U=1 , 2 , 3 , 4 , 4,  5 , 6 , 7 , 8  Y=1, 4 , 6Z=2 , 4 , 5 , 6clearly Y∩Z=  4

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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: Does the set S = span M22?

A: The given set is S=1100, 0011, 1001, 0111. Note that the above set is linearly independent set.

Q: Let A be the set of students in your math class, and B is the set of students at Indiana State…

A:

Q: Construct a Venn diagram illustrating the sets below. U={a, b, c, d, e, f, g, h} W={a, c, d,f} х-…

A:

Q: I, For A and B of Hhe univer sal ß subsets proside a in terse ct B set X, provide a formal prof for:…

A: Given: X is a universal Set. A and B are the subsets of Universal Set X. We have to prove that 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: 3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

A:

Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: Show by membership that for all sets A, B and C: А - (AnB) CА - В

A:

Q: 3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: , and C be subsets of a universal set U and suppose n(U) = 200, n(A) = 26, n(B) = 28, n(C) = 32, n(A…

A: Let A, B and C be the subsets of a universal set U . nU=200, nA=26,n(B) = 28, n(C) = 32, n(A ∩ B) =…

Q: Let {S,}EN is a disjoint seqeuence of measurable sets , then: US, µ(S,)

A: Given a statement

Q: Let {S,},EN is a disjoint seqeuence of measurable sets , then: HUS,

A:

Q: Here is a Venn Diagram with sets B, D, and the universal set U. RODI

A: Given that  Venn diagram of with sets B,D and the universal set U.

Q: Use the Venn diagram below to determine if C∪(A∩B)=(C∪A)∩(C∪B) and, if it is, what regions does the…

A: Given

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: Draw a Venn diagram for the symmetric difference of the sets A and B.

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Q: prove that the union of a countable set and an uncountable set is uncountable

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Q: Draw a venn diagram to represent the set A insersects B, but B has a line over it showing its a…

A: To represent the given combination of sets (A intersection B complement) in a Venn diagram

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

A: Given Venn diagram:

Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

A:

Q: The cardinality of a finite set A, denoted by Al, can provide the of A as equal to 21A

A:

Q: Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

A: We use set theory here: A: The set of sophomores at your school B: Set of students in discrete…

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Q: Let {$,}nEN is a disjoint seqeuence of measurable sets , then: 00 00 n=1

A:

Q: 2- Moke the definitions of open and closed sets. x =Larbic,d,eļ and ノ closed subsets of (x,T) space,…

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Q: Show that the union of two sets, each of measure zero, has measure zero

A:

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.