Question

What is the number of elements in the smallest equivalence relation over set A with |A|=n ?

Answer 1

Answer on question 38239 – Math – Abstract Algebra

What is the number of elements in the smallest equivalence relation over set A with $|A| = n$?

In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition.

Therefore the smallest equivalence relation on a set $A$ is

$$R\{(a, a) \mid a \in A\}$$

So, $n(R) = n(A) = n$.

Answer: n.