The area, demarcated with solid line, in the Venn’s diagram, shows the union of two sets denoted by (

Union of two sets |
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The sum of the numbers in the individual sets is generally greater than the numbers in the union. The reason is that union includes common elements only once. On the other hand, sum of the numbers of individual sets counts common elements once with each set – in total two times. Clearly, it is required that we deduct the numbers of elements, which are common to each set, from the sum of numbers of elements in individual sets. Hence,

Here, n(

Alternatively, we can approach this expansion in yet another way. See the representation of intersection of two sets. The union of two sets can be considered to comprise of three distinct regions. Three regions shown with different colors represent three “disjoint” sets. Clearly,

Union of two sets |
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However, we observe that if we add n(

and

Substituting for the numbers of the difference set in the equation for the numbers in the union set, we have :

**Numbers of elements in the union of “disjoint” sets**

Since there are no common elements between two disjoint sets, the intersection between disjoint sets is an empty set. Hence,