Union of Sets
2026-02-21 20:35 Diff
https://brightchamps.com/en-us/math/algebra/union-of-sets

When two or more sets are joined together, the combination of all their elements without repetition is known as the union of sets. The symbol “∪” is used to indicate it. 

Example:
If A = {7, 8, 1} and B = {1, 0, 3}.

Then,
A ∪ B = {0, 1, 3, 7, 8}  

  • How to find the union of sets? 


To better understand how to find the union of sets, let’s examine the following example. Since A = {c, d, e, f} and B = { x, d, y, z}, we have two sets, A and B. We must determine the components that make up the union of A and B.

According to the definition of the union of two sets, the resulting set includes all elements that are in set A, set B, or both.

  • Set A = {c, d, e, f}
  • Set B = {x, d, y, z}

Therefore, the union is {c, d, e, x, y, z}
Though d appears in both sets, it must be written only once because sets in a union do not include duplicate elements. 

  • How to represent union of sets in Venn diagram


Venn diagrams are used to illustrate or clarify the connections between the specified set of operations. They use circles to symbolize each set.

Let us examine how to depict the union of two sets to find the union of sets using the Venn diagram. The two provided sets, H and M, are subsets of a universal set, which is needed to illustrate their relationship. This union of the sets H and M is shown in the Venn diagram.

The union of sets H and M (which is H ∪ M) is represented by the blue area in the Venn diagram above. This includes all elements that are in H, in M, or both sets.

The Venn diagram is frequently used to depict the union between multiple sets, as long as the sets are finite, even though the union operation between two sets has been used here.

Example:
K ∪ U = {2, 5, 6, 7, 8, 9}
K =  {2, 5, 6}
U =  {7, 8, 9}

If set K contains {2, 5, 6} and set U contains {7, 8, 9}, then the union K ∪ U would be 
{2, 5, 6, 7, 8, 9}.