Union of sets

Definition:

The Union of two sets A and B is the smallest set, which contains all the elements of both sets and taking every element of both sets A and B, without repeating any element, or common elements being taken only once.

The symbol ‘∪’ used for the Union of two sets.

Symbolically, we write union of two sets A and B is

A∪B, and read as ‘A union B’.

A∪B={x: x∈A or x∈B}

shaded portion is A∪B

Union of two joint sets

if A and B are two joint sets and some common elements within them, that is A∩B ≠ 0, then 

Example: Let set A = { 1, 2, 3,} and 
                    set B = {3, 4, 5}

The Union of two sets A and B is the smallest set, which contains all the elements of both sets, and also
taking every element of both sets A and B, without repeating any element , 
we get,
                      A∪B = {1, 2, 3, 4, 5}

Set A∪B contains all the elements of set A and all the elements of set B, with no repetition of elements, and known as union of set A and B.

Element 3 in both sets A and B so we take element 3 only once.

                              A∪B∪C 

Example 1: Find union of given sets?

1. If A = {1, 2, 3, 4} and B = {1, 5, 3, 6, 7,}. 
Find union of set A and set B.

Solution: Elements 1 and 3 are common elements in both sets, or 1 and 3 are repeated, so, elements 1 and 3 taken only once. 

Therefore,  A∪B ={1, 2, 3, 4, 5, 6 7,}

Example 2: If P = {x, y, z} and Q= {∅}. Find union of set P and set Q

Solution: P∪Q ={x, y, z}

Union of any set with an empty set is the set itself.

Example 3: If A = {6, 7, 8, 9} and B = {1, 5, 3, 6, 7,}. Find union of set A and set B.

             A∪B = {6, 7, 8, 9, 1, 5, 3, 6, 7,}

Example 4: Find union of given sets, and draw a venn diagram to show A ∪ B ?

1. If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 5, 6}  and B = {1, 2, 3, 4}. 

Solution: A = {1, 2, 5, 6} and B = {1, 2, 3, 4}. 

∴ A∪B = {1, 2, 3, 4, 5, 6,}

A∪B