Sets

In general terms, a sets refers to a collection of things. In mathematics, a group of numbers, characters, variables, etc. can form a set. The objects within the set have certain common attributes that give the identity of that particular set. It means the objects contained in a set have some clear criteria that make them suitable for the part of a set. It can be said that a set is a container holding certain elements that has some common characteristics. The description of the set indicates this attribute or criteria that each of the items within the set must possess.

Representation of Set

A set comprises some objects that are called the elements of that set. A set is represented by a capital letter followed by an equal sign and then the elements are enclosed inside a pair of second brackets { }. The elements inside the brackets are separated by commas.

Let’s consider a set denoted by ‘S’ which is a collection of even numbers greater than ten and less than twenty. So the elements of the set ‘S’ are 12, 14, 16, and 18.

So this set is represented as S= {12, 14, 16, 18}.

The elements denoted by alphabets must be written in lowercase. One important point is that the elements in any set can be written in any order but there should not be any repetition of elements.

Classification of Sets

As per mathematical definition, sets can be classified into different types depending on the nature of elements contained in them.

• Equal set: Two different sets having identical elements.

For example, A= {a, b, c, d} and B = {a, b, c, d} are equal sets.

• Equivalent set: Two different sets having the same number of elements.

Two equivalent sets  P and Q can be represented as n(P) =n(Q)

• Subset: A subset of another set contains elements that can be found in the other set.
• Superset: A superset of another set means the latter is a subset of the former.

For example, for M= {2, 4, 6, 8, 10, 12} and N= {2, 4, 6, 8}, N is a subset and M is a superset.

• Singleton set: A set that contains only a single element.
• Null set: A set that does not contain any element.
• Finite set: A set containing only a definite number of elements.

For example, a set of odd numbers less than 10 is Z = {1, 3, 5, 7} is a finite set.

• Infinite set: The number of elements in this type of set is infinite.

For example, a set of all even numbers E= {2, 4, 6, 8…} up to infinite.

Cuemath

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