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:
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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.
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Let $$A = \left\{ {x:{x^2} – 10x + 16 = 0} \right\}$$ and $$B = \left \{{2, 8} \right\}$$, then $$A = B$$.