Equal Sets and Equivalent Sets – Definition and Example

Here you will learn definition of equal sets and equivalent sets with examples.

Let’s begin –

Equal Sets and Equivalent Sets

(i) Equal Sets :

Two finite sets A and B are equivalent if their cardinal numbers are same i.e. n(A) = n(B).

Where cardinal number means numbers of elements in a set.

(ii) Equivalent Sets :

Two sets A and B are said to be equal if every element of A is a member of B, and every element of B is a member of A.

If sets A and B are equal, we write A = B and A \(\ne\) B when A and B are not equal.

If A = {1, 2, 5, 6} and B = {5, 6, 2, 1}. Then A = B, because each element of A is an element of B and vice-versa. Note that the elements of a set may be listed in any order.

For Example : Let A = {1, 2, 3} and B = {a, b, c}

Then set A and set B are equivalent sets because n(A) = n(B) = 3. But not equal sets.