GATE1998-1.6

Question

Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is

• A. $n$
• B. $n^2$
• C. $1$
• D. $n+1$

Answer 1

Answer is $B$.

The largest equivalence relation will be when every element is related to every other element. So, $n \times n = n^2$ possible ordered pairs.

Comments

xpln?

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Explained..

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is there a difference withe these two statements:

Suppose A is a finite set with n elements.

Suppose A is a finite set of n elements.

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Nope

Answer 2

∣A∣ =n

Largest equivalence relation on set A = A ⨉ A

And the Number of elements in the Largest equivalence relation on set A = ∣A ⨉ A∣ = n^2

The correct answer is (B) n^2

Answer 3

Largest equivalent relation will be the Cartesian product of both the sets. so $n \times n=n^2$ is the answer