Examples of equivalent sets

Answer 1

equivalent sets are sets having the same number of elements

Example:

a= {dog, cat, buffalo, horse, cow} b= { lion, tiger, zebra, wolf, puma}

set a has 5 elements, so with set b which has 5 elements. so, sets a and b are equivalent sets.

Answer 2

For finite sets similarity simply requires both sets to have the same number of distinct elements (the same cardinality). For example, {1,2,3} and {a,b,c,a}. The second set appears to have 4 elements but, in fact, it has only three distinct elements - the same as the first.

Similarity of sets does get more complicated (and counter-intuitive) when dealing with infinite sets. It is probably not too hard to see that the set of odd integers (infinitely many) is similar to the set of even integers (infinitely many). But it is not so easy to see that the set of odd integers is similar to the set of ALL integers.

This is because you can define a mapping from the odd integers to all integers as:

2n-1 to n

Proving that this mapping is bijective (injective and surjective) shows that the two sets have the same cardinality.