We have a deck of cards. In this deck we have cards of the four different suits (clubs, diamonds, hearts and spades) with the numbers from 2 to 10 on them, for a total of 36 cards (face cards and aces have been excluded from the deck). Let A be the set of all cards with red suits (hearts and diamonds), and let B be the set of all the cards with a number smaller than 5. Let C be defined as A ∩ Bc. What is the complement of set C? provide sample space.

Q: Prove for all sets of A, B, that P(A) U P(B) is a subset of P(AUB).

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Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

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Q: 5. Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - UB, = N(A – B,).…

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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: Show by membership that for all sets A, B and C: A-(ANB) CA-B

A: Sets and relations

Q: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

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

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

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Q: The 61 students in a classical music lecture class were polled, with the results that 35 like…

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

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Q: Let A, B be any sets with ACB. Then O None of these O IP(BxB)|s|P(A×B)| O IP(A×B)=|P(B×B) O…

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

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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)…

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Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

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

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Q: 1. Of 25 microcomputers available in a supply room, 10 have circuits boards for a printer, 5 have…

A: According to Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

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Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

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Q: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: If A and B are sets and A is a subset of B, then A and B cannot be disjoint.

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Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

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: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose 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: If A is a countable set and B is a subset of A then

A: If A is a countable set and B is a subset of A then B is also a countable set since, every subset of…

Q: a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at…

A: Given: It is given that suppose that A is the set of sophomores at your school and B is the set of…

Q: 26. Draw the Venn diagrams for each of these combinations of the sets A, B, and C. b) ĀNBNT a) AN…

A: We are authorized to solve only one question please repost remaining questions Venn diagram

Q: Let A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and s, the…

A: We are given with multiple sub parts since our guideline is solve first three subparts.

Q: Let Ω be a set and A = {A ⊂ Ω : A is finite or Ac is finite }

A: given that Ω is a set and also given A ⊂Ω if Ω contains n elements  then A contains (n-1) elements…

Q: If A is a subset of a me

A: Given is a matric space X and a subset A. Then it is needed to prove that  A=x: each open sphere…

Q: 3* Consider three sets A, B, and C in a universal set U. Draw Venn diagrams of the following subsets…

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Q: If set K is such that n(K) = 3, then set K has 6 subsets

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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: Let A and Bbe seta Show hatAUB-U, hen ACB. e U a he ueal set

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Q: Let A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and S, the…

A: The set A=t,u,v,wS1 be the set of all subsets of A that do not contain wS2 be the set of all subsets…

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: Let the universal set U be a standard deck of 52 playing cards. Let E be the set of all even…

A: The intersection of two or more given sets is the set of elements that are common to each of the…

Q: (4) How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all…

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

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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: Use Venn diagrams to verify that if A is contained inB, then A ∩ B = A and A ∩ B = ∅.

A: Venn Diagram: Euler Venn Diagram or commonly known as Venn Diagram, is a diagrammatic representation…

Q: Prove that for every n E N if A is a set with n elements, then the power set of A, P(A), has 2"…

A: The set P(A) contains every possible subset of A, including the empty set and the set A itself.

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

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

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