GATE | GATE CS 1997 | Question 58

Let R be a reflexive and transitive relation on a set A. Define a new relation E on A as

E= {(a,b) ∣ (a,b)∈R and (b,a)∈R }

a. Prove that E is an equivalence relation on A.
b. Define a reason ≤ on the equivalence classes of E as E1≤E2 if  ∃a,b such that a∈E1, b∈E2 and (a,b)∈R. Prove that ≤ is a partial order.



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