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

1. $n$
2. $n^2$
3. $1$
4. $n+1$

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.
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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

∣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

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