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Empty Set

Let us consider the set E of all odd integers which satisfy the equation x2 = 4. We know that there is no odd integer which satisfies the equation x2 = 4; therefore, E contains no element. Such a set is called an empty set or null set or void set. The null set or empty set is denoted by the symbol φ or {}.
Illustration 1
Let A be the set of people on the earth who are older than 500 years. According to known statistics, there is no such person. Hence, A is an empty set.

Illustration 2
Let C denote the set of all cars, which can run at a speed of light. Since, there is no such car, C is an empty set.

Illustration 3
The eighth colour of the rainbow. There are only seven colours in a rainbow. Hence it is an example for an empty set.

The set {φ} is not an empty set as it contains element φ.

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