Set S= {(x, y) e R x R: y – x is an integer}. a) Prove that S is an equivalence relation on R. b) List four members of [7]. c) Which real numbers belong to [-17]? %3D

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A: The solution is as follows:

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Q: Consider the equivalence relation {(r, y) | a = y (mod 6)}| on the set {n e Z| – 9 <n< 15}| Use the…

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A: Equivalence relation and classes

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Q: Let ~ be defined on the set X = {0,1,2,3,4,5,6,7,8,9} by x ~ y + x2 = y? mod 5. Prove that is an…

A: Equivalence relation are those which are reflexive symmetric and transitive

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Q: ) Let S = {(x, y) E R × R: y – x is an integer} a) Prove the S is an equivalence relation on R b)…

A: Given, S=x,y∈R×R: y-x is an integer

Q: Let R be a relation on Z defined by R = {(p, q) E Z × Z |p – q is a multiple of 3}. (a) Show that R…

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A: We need to prove 1) Reflexive 2) symmetric 3) transitive.

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Q: Prove the understated statements concerning the relation &lt; on the set Z of all integers . If x…

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Q: Let R and S be reflexive relations over set A. Prove or disprove that RnS is reflexive

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Q: 3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples.

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Q: 8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d)…

A: Equivalence relation