GATE | GATE-CS-2007 | Question 2

Let S be a set of nelements. The number of ordered pairs in the largest and the smallest equivalence relations on S are:
(A) n and n
(B) n2 and n
(C) n2 and 0
(D) n and 1


Answer: (B)

Explanation:

Consider an example set, S = (1,2,3)

Equivalence property follows, reflexive, symmetric
and transitive

Largest ordered set are s x s = 
{ (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3,1) (3,2) 
(3,3) } which are 9 which equal to 3^2 = n^2

Smallest ordered set are { (1,1) (2,2) ( 3,3)}
which are 3 and equals to n. number of elements.


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