Given the set S = {a,b,c,d) and that a ~ b and d~ b. Which of the following relations must also be true if ~ is to be an equivalence relation on S?

Q: Let R and S be two equivalence relations on a nonempty set, and T their intersection. What's their…

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Q: Let A = {1, 2, 3, 4, 5, 6} and let S = P (A), 1 set of A. the power a. For a, b e S, define a ~ b if…

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Q: Let A = {2,3,4,...,17,18). Let R be the equivalence relation on AxA, defined by (a,b)R(c,d) if and…

A: Let A = {2,3,4,.......... 17,18].Let R be the equivalence relation on AXA, defined by (a,b)R(c,d) if…

Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: Answer the following question accordingly:

A: Given set is  B={1,2,3,4}

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: 4. Let A = (a, b,c, d). Suppose R is an equivalence relation on A. Suppose R has three equivalence…

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

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: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: 7. Let S = {1,2,3, ...,8}. Let R be the relation on S defined by the following: %3D xRy + xy is a…

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Q: Determine whether or not the relation R on the set of all people is reflexive, netric,…

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Q: Let S = {1;2;3;4}, and suppose that ~ is an equivalence relation on S: You are given the information…

A: Given: S=1, 2, 3, 4 and ~ is an equivalence relation on S. Also we have 1~2 and 2~3. To show: There…

Q: 4. Let A = {a, b, c, d}. Suppose R is an equivalence relation on A. Suppose R has three equivalence…

A: To Determine: write R as a set .describe then all   Given: let A={a,b,c,d} suppose R is an…

Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

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Q: S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and…

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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: 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…

Q: In each item below, verify that ~ is an equivalence relation on the given set. (a) Let S = Z x N.…

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Q: and B = {Thaddeus, Peter} be the set of male members. Let R be the relation between the sets A and B…

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Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: Define a binary relation on the set S=(-3, -2, -1, 1, 2, 3} as follows: R= {(a,b) ab>0} %3D a. Find…

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Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

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: Which of the following statements about equivalence relations and partial ordering is/are ALWAYS…

A: The objective is to find which of the following statements about equivalence relations and partial…

Q: Let A, B, and C be sets. Prove or disprove: If R and S are equivalence relations on A, then S o R is…

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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

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

Q: Let A = {a, b, c, d, e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

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Q: (d) Justifying your answer, find the smallest set of related pairs which must be added to R in order…

A: We know that a relation is called an equivalence relation if it is reflexive, symmetric and…

Q: a. Let A = The set of numbers involve in your college ID. And R = {(x, y)1+ 2 divdes (x3 + y} be a…

A: Part (a) Write Cartesian form of set R: A=0,1,3,5,7R=x,y|⇔2 divides…

Q: Consider the set S = {A, B, C, D}: For each of the following relations on S, determine whether it is…

A: Definitions: