Venn Diagram & Principle of Inclusion and Exclusion

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Venn Diagram & Principle of Inclusion and Exclusion

Suppose there are $N$ objects out of which there are exactly $N_a$ objects of type $a$ and $N_b$ objects of type $b$ . Also, suppose there are exactly $N_{ab}$ objects that are of both type $a$ AND $b$ . Then, how many objects are NOT of type $a$ OR $b$ ?

The Venn diagram above illustrates this case.The number of objects outside the two oval regions equals $N - (N_a + N_b - N_{ab}) = N - (N_a + N_b) + N_{ab}$ , and this is the answer.