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

The correct option is B $n^2$

$A$ is a finite set with $n$ elements. The largest equivalence relation of $A$ is the cross-product $A\times A$ and the number of elements in the cross product $A\times A$ is $n^2$.