# 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 $A = B$.