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A collection of well-defined objects is called a set.


Each object has some properties naturally. If properties of an object is compared with the properties of other objects, either one or more or all properties may be same. The collection of such objects is called a set.


Study the following examples to understand how to define and form a set mathematically.


Set of apples

You are seeing three apples in which an apple is a green apple and the remaining two apples are red colour apples.

All are apples. It is a common property of them. If you consider it and ignore their color, the collection of them is called a set.

If you consider its colour, they cannot form a set. The collection of two red apples form a set and the remaining green apple form another set.


Set of footballs

There are some footballs in a football stadium and the total footballs is $8$.

All $8$ balls are footballs. Hence, the collection of all eight footballs is a set.

If we consider the size of the footballs, the collection of all eight footballs is not a set because three footballs are in actual size and the other five footballs are in small size. Therefore, the collection $3$ footballs is a set and the collection $5$ footballs is another set.


Set of cars

Observe the both cars. The properties such as colour, model and everything are same. Hence, the collection of both cars is a set.

The above examples give you an idea about defining a set mathematically according to set theory.

Remember one thing while defining a set; if you want to define a set on the basis of either one or more properties, the objects should have same property or properties commonly. Otherwise, the objects cannot form a set mathematically.


Learn how to represent a set graphically and mathematically in mathematics.

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