Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a - b is divisible by 13 and x = y. Then R is O oot a reflexive relation O an equivalence relation O not a transitive relation O not a symmetric relation

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Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

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Q: Subject: Set Theory

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A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

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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

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A: According to the given information, it is required to solve the question 10.

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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