Set Notation for Set Operations

Different set notation for set operations include union, intersection, subset, difference, symmetric difference and complement of sets.

Union

Union (U) is represented by ∪ set notation. Union is a binary operations on two sets that includes all the elements of both sets. It is mathematically represented as for two sets A and B, A ∪ B = {x: x∈A or x∈B}.

Example: Find the union of set X = {2, 3, 4} and Y = {4, 5, 6}.

Solution:

X = {2, 3, 4}

Y = {4, 5, 6}

X ∪ Y = {2, 3, 4, 5, 6}

Intersection

Intersection (∩) is represented by ∩ set notation. Intersection is a binary operation on two sets that includes the common elements of both sets. It is mathematically represented as for two sets A and B, A ∩ B = {x: x∈A and x∈B}.

Example: Find the intersection f set X = {2, 3, 4} and Y = {4, 5, 6}.

Solution:

X = {2, 3, 4}

Y = {4, 5, 6}

X ∩ Y = {4}

Difference

Difference ( \ ) is represented by \, – set notation. Difference is a binary operation on two sets that includes elements of first set that are not present in second set. It is mathematically represented as for two sets A and B, A – B = {x: x∈A and x∉B}.

Example: Find the difference of set X = {2, 3, 4} and Y = {4, 5, 6}.

Solution:

X = {2, 3, 4}

Y = {4, 5, 6}

X – Y = {2, 3}

Subset

The subset of set is represented by ⊆ set notation. The set B is called the subset of A if all the elements of set B are present in set A. It is mathematically represented as for two sets A and B, B ⊆ A = {x: x∈A ∀ x∈B}.

Example: Find whether X is subset of Y or not where set X = {2, 3, 4} and Y = {2, 3, 4, 5, 6}.

Solution:

X = {2, 3, 4}

Y = {2, 3, 4, 5, 6}

Since Y includes all the elements of X

Therefore, X ⊆ Y

Complement

Complement (A’) of set is represented by (Set)^c set notation. Complement of a set includes the elements of universal set that is not present in the given set. It is mathematically represented as for a set A A^c = {x: x∉A}.

Example: Find the complement of set X = {2, 3, 4} and U = {2, 3, 4, 5, 6}.

Solution:

X = {2, 3, 4}

X^c = {5, 6}

Set notation refers to the different symbols used in the representation and operation of sets. The set notation used to represent the elements of sets is curly brackets i.e., {}.

In this article, we will explore set notation, set notations for set representation and set operations. We will also cover the set notation table and solve some examples related to set notation.