# Objects Form a Set

How to state that whether the objects form a set or not?

1. A collection of ‘lovely flowers’ is not a set, because the objects (flowers) to be included are not well-defined.

Reason: The word “lovely” is a relative term. What may appear lovely to one person may not be so to the other person.

2. A collection of “Yellow flowers” is a set, because every red flowers will be included in this set i.e., the objects of the set are well-defined.

3. A group of “Young singers” is not a set, as the range of the ages of young singers is not given and so it can’t be decided that which singer is to be considered young i.e., the objects are not well-defined.

4. A group of “Players with ages between 18 years and 25 years” is a set, because the range of ages of the player is given and so it can easily be decided that which player is to be included and which is to be excluded. Hence, the objects are well-defined.

Now we will learn to state which of the following collections are set.

State, giving reason, whether the following objects form a set or not:

(i) All problems of this book, which are difficult to solve.

Solution:

The given objects do not form a set.

Reason: Some problems may be difficult for one person but may not be difficult for some other persons, that is, the given objects are not well-defined.

Hence, they do not form a set.

(ii) All problems of this book, which are difficult to solve for Aaron.

Solution:

The given objects form a set.

Reason: It can easily be found that which are difficult to solve for Aaron and which are not difficult to solve for him.

Hence, the objects form a set.

(iii) All the objects heavier than 28 kg.

Solution:

The given objects form a set.

Reason: Every object can be compared, in weight, with 28 kg. Then it is very easy to select objects which are heavier than 28 kg i.e., the objects are well-defined.

Hence, the objects form a set.

The members (objects) of each of the following collections form a set:

(i) students in a class-room

(iii) counting numbers between 5 to 15

(iv) students of your class, which are taller than you and so on.

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams