## A union B formula

In sets, ‘U’ stands for the term union and A U B means any element in set A or set B. Hence an A U B set will contain all the elements present in both A and B. It can simply be found by putting all the elements of set A and set B together and removing all the common/duplicate elements. Hence even though there is a formula that can be put to use, the union of two sets can be calculated without it also.

However, the formula makes the calculations easier and looks like the following:

n (A U B) = n (A) + n (B) – n (A ∩ B)

where,

n (A U B) =number of elements in A U B

n (A) =number of elements in A

n (B)=number of elements in B

n (A ∩ B) =number of elements that are present in both set A and set B (duplicate terms)

We must remember that n(A) + n(B) is different from n (A U B) because the latter includes the common terms between them as well.

## Solved Example

**1. Example 1: If A = {2,5,8,9} and B = {3,5,8,11}, then calculate A U B.**

**Solution:** Given that:

A = {2,5,8,9}

B = {3,5,8,11}

We use the A U B formula by simply writing all the terms present in set A and set B together and no element is repeated.

So, A U B = {2,5,8,9} U {3,5,8,11} = {2,3,5,8,9,11}

Note: It is not necessary for the elements to be in order.

**Answer:** A U B = {2,3,5,8,9,11}

**2. Example 2: Find the number of elements in A U B if n(C) = 25, n(D) = 10 and n (C ∩ D) = 12.**

**Solution: **To find the number of elements in C U D, we will use the formula n (C U D) = n(C) + n(D) – n (C ∩ D).

n (C U D) = 25 + 10 – 12

= 35 – 12

= 23

**Answer: **Hence, the number of elements in C union D is23.