Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. -Maths 9th

Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. -Maths 9th
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Answer :

R = {(x, y)}: x and y are graduates of same university, x, y ∈ {All graduates of India}. R is reflexive as (x, x) ∈ R, since x and x are graduates from the same university. R is symmetric as (x, y) ∈ R ⇒ x and y are graduates from the same university. ⇒ y and x are graduates from the same university ⇒ (y, x) ∈ R. R is transitive as (x, y) ∈ R and (y, z) ∈ R ⇒ x and y are graduates from the same university and y and z are graduates from the same university ⇒ x and z are graduates from the same university ⇒ (x, z) ∈ R. R being reflexive, symmetric and transitive is an equivalence relation.
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