What is equivalent sets and their examples?

Answer 1

Two sets are equivalent if there exists a one-to-one mapping from the elements of one set to the other. It is quite easy to see that for finite sets this requires the two sets to have the same number of distinct elements.

So, for example, C = {Red, Blue, White, Red, Red} and N = {2, 4, 5} are equivalent sets. One possible mapping is

Blue -> 1

Red -> 2

White -> 3

It can get confusing when you get to infinite sets. Consider the set of all positive integers, N, and all positive even numbers, E. You might think that they cannot be equivalent because the set N contains all of E and it also has all odd number in it.

However, the mapping: f, from N to E given by f(x) = 2x is one-to-one and therefore the two sets are equivalent.