Let A be a set and R = {(x, x) : x ∈ A} be the is-equal-to relation on A. Prove that a relation S on A is an equivalence relation and a partial ordering if and only if S = R.

Q: 4. Let R be a relation on the set of all integers. xRy iff x - y = 3m for some integer m. Show that…

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Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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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 X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

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Q: Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and…

A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

Q: 1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check…

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Q: Let A = {-1,0,1} and R be a relation on A such that R = {(a,b)|a² =b}. Select all properties of this…

A: A relation R on a set A is basically a subset of A×A. For a non-empty set A and a relation R on it;…