Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x – y)}. Verify R is an equivalence relation? ...

Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,1), (1,2), (1,4), (2,2),…

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

A: Since you have asked multiple questions, we will solve the Question Q (a) and (b) for you. If…

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

A: Explanation of the answer is as follows

Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,b),(b,b),(b,c)(c,a)(c,c) and…

A: Given set is A = {a, b, c, d} and the relation R on set A is R = {(a, b), (b, b), (b, c), (c, a),…

Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) E…

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Q: Define a relation on Z by x ~ y if and only if x + 2y is divisible by 3. Show that this relation is…

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Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: Consider the following relation on {1,2,3,4}. Check is equivalence or not? R= {(1, 1), (1, 2), (2,…

A: Follow next step

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 3. Let S = {1, 2, 3, ...}. Let R be a relation on he set S x S defined by (a, b) R (c,d) ⇒…

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Q: (3) Let S be the equivalence relation on {0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

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Q: Let A = {1, 2,3, 4}. The following relation R is an equivalence relation on A: R=…

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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: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

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Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

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Q: It is based upon properties of relations. *Explanation is mandatory. Check whether the following…

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Q: Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3,…

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Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.