###### Question 7056 – Big-Data

November 9, 2023###### Question 4075 – UGC NET CS 2005 Dec-Paper-2

November 10, 2023# Question 9226 – GATE 2007

Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are:

Correct Answer: B

Question 2 Explanation:

A relation is said to be equivalent relation if it satisfies,

→ Reflexive

→ Symmetric

→ Transitive

Let a set S be,

S = {1, 2, 3}

Now, the smallest relation which is equivalence relation is,

S×S = {(1,1), (2,2), (3,3)}

= 3

= n (for set of n elements)

And, the largest relation which is equivalence relation is,

S×S = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

= 9

= 3

= n

→ Reflexive

→ Symmetric

→ Transitive

Let a set S be,

S = {1, 2, 3}

Now, the smallest relation which is equivalence relation is,

S×S = {(1,1), (2,2), (3,3)}

= 3

= n (for set of n elements)

And, the largest relation which is equivalence relation is,

S×S = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

= 9

= 3

^{2}= n

^{2}(for set of n elements)n and n

n

^{2}and nn

^{2}and 0n and 1

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