Let X = {1, 2, 3, 4, 5, 6) and S= {(1, 2), (3, 4), (5, 6)). Which of the following types of mathematical object could S be? a partition of X b. an equivalence class of an equivalence relation on X C. a relation on X a. d. a permutation of X

Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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Q: 4 Elephants and frogs, In this problem, A is the set of all animals, E is the set of all elephants…

A: Given that, A is the set of all animals, E is the set of all elephants and F is the set of all frogs…

Q: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: Questions: 1. Let A = {1,2,3,4,5). Let F be the set of all functions from A to A. Let R be the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: Let A = {1, 2, 3, 4, 5, 6}, and consider the following equivalence relation on A: R = {(1, 1),  (2,…

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Q: Let R1 and R2 be two different relations on the same set A. If R1 - R2 is reflexive then R1 is…

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Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1),…

A: Reflexive: If every element in set A is related to itself, i.e., (a, a) ∈ R for every a in…

Q: 2. Let A = {1,2, 3}, B = {4,5, 6}, R = {(1,4), (1, 5), (2,5), (3, 6), and || %3D S = {(4,5), (4, 6),…

A: Given set in the question are  A=1,2,3B=4,5,6R=(1,4),(1,5),(2,5),(3,6)S=(4,5),(4,6),(5,4),(6,6)Then…

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

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Q: Find the area of each circle, given the radius r or the diameter d. Leave your answer in tems of t.

A: See the detailed solution below.

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

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Q: Let R and S be relations defined on the set of {8, 1, 2, 7}. R = {(1,8), (7, 8), (8, 1), (7, 7)}. S…

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Q: Which ONE of the following represents an equivalence relation on the set of integers? Vx.y€Z, xRy if…

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Q: Let A = {1, 2, 3, 4, 5, 6} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 3), (3, 2)}.…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

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Q: Let R and S be relations defined on the set of {9,3, 1,0}. R = {(1,1), (9, 3), (1,3), (9,0)}. S =…

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Q: Let A and B be any two sets. A binary relation from A to B is i. CAXB ii. SANB CAUB Non of these…

A: Firstly we define binary relation from set A to set B, and then conclude the answer.

Q: Let A = {1,2,3,4,5,6}, and consider the following equivalence relation on A: R = {(1, 1), (2, 2),…

A: Given that A= { 1 , 2 , 3 , 4 , 5 , 6} And the equivalence relation on A R = { (1,1) ,(2,2) ,(3,3)…

Q: Let X = {1, 2, 3, 4}. Let R = {(1, 3), (2, 1), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (a, b) },…

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Q: Let A be a set and R and S be relations on A. Dene the relation R + S on A by R + S = (R-S) […

A: Let A be a set and R and S be relations on A. Define the relation R + S on A by R + S = (R-S) ∪…

Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…

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Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: 2. Let A={1, 2, 3, 4, 5, 6} and let R be a relation on A defined as follows: Va,be A, (a,b)…

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Q: Let X = {1, 2, 3, 4, 5, 6}. Which of the following could be an equivalence class of an equivalence…

A: Equivalence class on a set