Union of Set (AUB) Example Problems

In set theory, the union of a collection of sets is the set of all distinct elements in the collection. Union is denoted by the symbol 'U'. A union B is represented as (AUB). It is one of the fundamental operations through which sets can be combined and related to each other. Sets cannot have duplicate elements, so the union of the sets {1, 2, 3} and {2, 3, 4} is {1, 2, 3, 4}. Here are two simple Union of set (AUB) examples which helps to find the values for union of 2 sets.

Example 1:

Let us consider the problem: Set of elements in A={3,4,5,6} and set of elements in B ={1,2,3,5,8,9,10.} Find AUB

Solution:

We can calculate the Union of sets A and B(AUB) using the given formula.

Formula:

Union of Two Sets
A∪B = {a1,a2,a3,a4,...,an} with ai∈A or ai∈B,i=1,2,3,...n

Where, A and B represents the set A and set B

Substituting the values in the formula, Joining elements in A and B, we have 1,2,3,4,5,6,8,9,10

Hence, the value of Union of sets A and B (AUB) is 1,2,3,4,5,6,8,9,10.

Example 2:

Let us consider the problem: Set of elements in A={0,1,11,23,56} and set of elements in B ={ 23,10,90}. Find AUB

Solution:

We can calculate the Union of sets A and B(AUB) using the above given formula.

Substituting the values in the formula, Joining elements in A and B, we have 0,1,10,11,23,56,90

Hence, the value of Union of sets A and B(AUB) is 0,1,10,11,23,56,90.

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