Consider the relation R = {(a,b) | a is congruent to b mod 3} on set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the equivalence classes of R? O (1, 4, 7, 10}, (2, 5, 8), (3, 6, 9} O {1, 2, 4, 5, 7, 8, 10}, {3, 6, 9} O {1, 5, 9}, (2, 6, 10}, {3, 7}, {4, 8} O {2, 4, 6, 8, 10}, {1, 3, 5, 7, 9}

Q: With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Question 33 With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is…

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Q: R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S =…

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Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: The cardinality of { Ø, 1, 2, 2, {1, 2}} is

A: We need to find the cardinality of { ϕ, 1,2,2,{1,2}}.

Q: the sets  [0,1] and  [0,1/2)∪(1/2,1] have the same cardinality, give an explicit bijection to show…

A: We will define a bijection from the set J  = [ 0 , 12 ) ∪(12 , 1]   to the set I =0 ,1   First we…

Q: Let A= {1,2,3,4,5,6} and B={2,4,6,8}. what is the cardinality of A ∩ b?

A: Cardinality of a intersection

Q: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: And what would be the 15 equivalence relations? And what does "up to isomorphism" mean?

A: Ans-In this question we have to determine   all possible equivalence relations on the set…

Q: Let A = {1, 2, 3, 4, ..., 20}. What is the cardinality of the power set of A, P(A)?   Fill in the…

A: Cardinality of Set --: The Cardinality of a set is the total number of unique elements in the set.…

Q: 2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set…

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Q: Consider the relation R on the set A = {-6, –2,0,1, 4, 5, 6, 7, 15}, defined according to the…

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

Q: The relation R on the set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) is defined by R= {(x,y) E AXA: xmod…

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Q: (x, y)R (u, v) if xv, yu. Let Pbe the set of equivalence classes of Z × (Z – {0}) modulo R. For (a,…

A: GIVEN  let ℝ be the equivalence relation on ℤ×ℤ-0 given by x,yRu,v if xv=yu let P be the set of…

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

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Q: Let R be a binary relation on A={1,2,3,43 defined a is related with b) if a²-b² is divisble by 3.…

A: Bartleby Guideline: According to Bartleby's guideline I can solve the first three subparts at a time…

Q: Suppose p and o are relations defined on S = {1, 2, 3, 4} by the sets p = {(2, 2), (3, 2), (3, 4),…

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Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…

A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…

Q: Indicate the partition of the set A={ x integer: 2 ≤ x ≤ 12 } resulting from the equivalence…

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Q: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…

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Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: Let R = {(a, b) | a = b (mod 3)} be an equivalence relation on the set of integers Z. What are the…

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