What are equivalent sets?

Two sets are said to be equivalent if they have the same number of elements in each set. Two equivalent sets are represented symbolically as A~B. Equal sets are always equivalent, but two equivalent sets are not always equal.

If set A = {1,2,3,4,5} and set B = {a,b,c,d,e}, then n(A) = 5 and n(B) = 5. Hence, n(A) = n(B), or the number of elements in set A is equal to the number of elements in set B. Thus, set A is equivalent to set B, or A~B.

If set A = {1,2,3,4,5} and set B = {5,4,3,2,1}, then both sets have the same number of elements as well as identical elements. Such sets are called equal sets. They also have the same number of elements in different order. Hence, n(A) = n(B) = 5, or A~B.