Two sets A and B are said to be equal(=) if they have the same elements. The elements may not be in the same order. If an element appears n times in one set, then it must also appear n times in the other set.

Mathematically, two sets A and B are equal if

• For each a ∈ A, there exists an element b ∈ B.
• n(A) = n(B) i.e. cardinality of A is equal to cardinality of B.

Examples ⇒

{ 1, 2, 3, 4 } = { 1, 3, 4, 2 }

{ 1, 1, 2, 2, 2, 4, 5 } = { 1, 4, 1, 2, 5, 2, 2 }

{ 1 ,2 ,3 ,4 } ≠ { 1 ,2 ,3 ,4 ,4 }

Two equal sets can be thought of as a mirror image of each other. At any given moment of time, each and every element in set A must have an exact copy of itself in set B and that copy in B must not be a copy of any other element in set A.

Imagine a set of books on mathematics, physics and biology kept on a table. The collection forms a set. When you re-arrange the placement of books on the table without adding or removing any book, the new order of books forms a collection that is equal to the prior set. This should give a mental idea of what equal sets means.