Equality of Sets

Equality of sets is defined as set A is said to be equal to set B if both sets have the same elements or members of the sets, i.e. if each element of set A also belongs to each element of set B, and each element of set B also belongs to each element of set A.

Mathematically it can be written as A \subset B and B \subset A. In this case we write it as A = B. If there is at least one elements of B which is not in A, then A is not equal to B and we write A \ne B.

 

Example:

  1. Let A = \left \{ {2, 4, 6, 8} \right \} and B = \left \{ {8, 4, 2, 6} \right \}, then A = B because each element of set A that is 2, 4, 6, 8 is equal to each element of set B; that is 8, 4, 2, 6. If we rearrange the elements of the set it will remain the same.
  2. Let A = \left\{ {x:{x^2} - 10x + 16 = 0} \right\} and B = \left \{{2, 8} \right\}, then A = B.