GATE | GATE-CS-2007 | Question 2

Let S be a set of n elements. 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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