A union B Formula - A U B, Venn Diagram, Examples (2024)

The union of two sets A and B is a set that contains all the elements of A and B and is denoted by A U B (which can be read as "A or B" (or) "A union B"). A union B formula is used to find the union of two sets A and B. The union can be found by just putting all the elements of A and B in one set and removing duplicates. i.e., A U B can be found without using the A union B formula also.

Let us learn about the A union B formula with a few examples in the end.

1.What Is the A Union B Formula?
2.Number of Elements in A union B Formula
3.Complement of A Union B Formula
4.What is A union B Probability Formula?
5.Union with 3 Sets
6.FAQs on A Union B Formula

What Is the A Union B Formula?

The union of two sets is represented by writing the symbol "U" in between the two sets. The formula for A union B means that any element that is present either in A or in B is present in A ∪ B. By using the above definition, the A union B formula is,

A ∪ B = {x : x ∈ A (or) x ∈ B}

A union B Formula - A U B, Venn Diagram, Examples (1)

This is the Venn diagram representing "A union B" where it represents the entire portion shaded in "Orange" color.

Example: If A = {1, 2, 3, 4} and B = {3, 4, 5} then calculate A ∪ B.

Solution:

To calculate A ∪ B, just write all the elements of A and B in a set and remove duplicates. Then we get:

A ∪ B = {1, 2, 3, 4, 5}

Number of Elements in A union B Formula

Suppose we have two sets A and B. Now, A U B consists of elements of both sets A and B, taken one at a time (leaving duplicates). We have the following representations:

  • 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 common to both A and B

n(A) + n(B) gives the total number of elements that are in A and the elements in B including the elements that are common. This implies that the number of common elements is counted twice. Hence, to balance that and make sure that all the elements are counted just once, we subtract n(A ∩ B) from n(A) + n(B) and hence the formula for the number of elements in A U B is:

n(A U B) = n(A) + n(B) - n(A ∩ B)

Complement of A Union B Formula

The complement of a set is the difference of the universal set and the given set. In the same way, the complement of A U B (which is denoted by (A U B)') is "universal set - (A U B)". It is shown by the Venn diagram below:

A union B Formula - A U B, Venn Diagram, Examples (2)

Here, the complement of A union B is the portion shown by Blue colour. This can be easily calculated using one of De Morgan's laws as:

(A U B)' = A' ∩ B'

What is A union B Probability Formula?

Using the same logic as above and to avoid counting the same elements twice, we have the formula for P(A U B) (the probability formula of A union B) as:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

If A and B are mutually exclusive events, then we have P(A ∪ B) = P(A) + P(B) as P(A ∩ B) = 0.

Union with 3 Sets

Here are multiple combinations of union and intersection involved with 3 given sets A, B, and C.

A Union B Union C: The formula related to A U B U C is and is given by n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C). It is shown by the following Venn diagram in Orange colour.

A union B Formula - A U B, Venn Diagram, Examples (3)

A Intersection B Union C: This can mathematically be written as:A n ( B U C) and here is the Venn diagram representing it.

A union B Formula - A U B, Venn Diagram, Examples (4)

Important Notes on A union B Formula:

  • A U B = {x : x ∈ A (or) x ∈ B}
  • n(A U B) = n(A) + n(B) - n(A ∩ B)
  • P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
  • A U B = B U A

Related Topics:

  • Intersection of Sets
  • A∩B Formula

FAQs on A Union B Formula

What is A union B Formula in Math?

By using the definition of A U B, the A union B formula is, A U B = {x : x ∈ A (or) x ∈ B} which implies A U B consists of elements that are either in A or in B or in both.

How Do You Calculate AUB?

A U B can be calculated by taking the elements of A and the elements of B and considering the elements that are common in both A and B only once and combining them in one set.

Is the Union of Sets Commutative?

Yes, the sets are commutative with respect to the operation "union". For any two sets A and B, we always can prove that A ∪ B = B ∪ A.

What is the Union of A and B?

The union of two sets A and B is a set that contains all the elements of A and B taken one at a time and is denoted by A U B.

What is A union B Whole Complement Formula?

The formula for A union B whole complement formula is given by, (AUB)c = Ac ∩ Bc. It is also one of the De-Morgan's Laws of Union of Sets.

Can the A Union B Formula be Used for More than Two Sets?

Yes, the A union B formula can be extended to find the union of more than two sets. For example, the formula for the union of three sets A, B, and C would be A ∪ B ∪ C = (A ∪ B) ∪ C.

What is the Formula for the Cardinality of A union B?

The cardinality (number of elements) of A union B can be calculated by counting the elements in A and B and taking the elements that are common only once. The formula for the cardinality of A union B is n(A U B) = n(A) + n(B) - n(A ∩ B).

A union B Formula - A U B, Venn Diagram, Examples (2024)

FAQs

A union B Formula - A U B, Venn Diagram, Examples? ›

A union B Complement Examples

Solution: We have A = {2, 4, 6}, and B = {1, 3, 5}, then A U B is given by, A U B = {1, 2, 3, 4, 5, 6}, then A union B complement is given by, (A ∪ B)' = U - (A ∪ B)

What is an example of aub? ›

A union B Complement Examples

Solution: We have A = {2, 4, 6}, and B = {1, 3, 5}, then A U B is given by, A U B = {1, 2, 3, 4, 5, 6}, then A union B complement is given by, (A ∪ B)' = U - (A ∪ B)

What is A ∩ B in Venn diagram? ›

Venn Diagram Symbols
Venn Diagram SymbolsExplanation
The intersection symbol - ∩A ∩ B is read as A intersection B. Elements that belong to both sets A and B. U is the universal set.
The complement symbol - A c or A'A' is read as A complement. Elements that don't belong to set A. U is the universal set.
1 more row

How do you find AUB with A and B? ›

What is the Formula for the Cardinality of A union B? The cardinality (number of elements) of A union B can be calculated by counting the elements in A and B and taking the elements that are common only once. The formula for the cardinality of A union B is n(A U B) = n(A) + n(B) - n(A ∩ B).

What is the formula of AUB? ›

Formula for Number of Elements in A union B

Consider two sets, A and B, such that the number of elements in the union of A and B can be calculated as follows. n(A U B) = n(A) + n(B) – n(A ∩ B)

What does ∩ mean in Venn diagrams? ›

Venn Diagrams Symbols

Intersection (∩): Represents all elements shared or common within the selected sets or groupings. Intersection represents shared elements (in the middle) within sets X and Y. Complement (XC): Represents whatever is not represented in a particular set; in this case, everything not in set X.

What does a ∪ B look like? ›

Union of two sets: ∪

(Don't confuse this symbol with the letter “u.”) This is a two-circle Venn diagram. The green circle is A, and the blue circle is B. The complete Venn diagram represents the union of A and B, or A ∪ B.

What is the union formula example? ›

Example 1: Find the union of sets A and B, where A = {0,1,2,3,4} and B = {13}. The union of two sets contains all elements that are present in the first set, the second set, or elements are in both sets. Thus, A ∪ B = {0,1,2,3,4,13}. Answer: A ∪ B = {0,1,2,3,4,13}.

What is an example of a union? ›

Another example of a labor union is the International Brotherhood of Teamsters, which represents a variety of blue-collar workers, including freight drivers, warehouse workers, sanitation workers, and construction workers. The union negotiates pay rates, benefits, and workplace conditions for its members.

What is A∩B example? ›

For any two sets A and B, the intersection, A ∩ B (read as A intersection B) lists all the elements that are present in both sets (common elements of A and B). For example, if Set A = {1,2,3,4,5} and Set B = {3,4,6,8}, A ∩ B = {3,4}. Let us earn more about the properties of the intersection of sets along with examples.

How to get aub? ›

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.

What is an example of AUB sets? ›

For example, if set A = {4, 7, 9, 3, 10} and set B = {1, 4, 10, 11, 20} the union of sets A and B, written as A ∪ B , results in the set A ∪ B = {1, 3, 4, 7, 9, 10, 11, 20}.

What is AUB in Venn diagram? ›

Union. The union of a Venn diagram is the numbers that are in either Set A or Set B. The union of the above example is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 as it's the numbers that appear in either of the circles. We write it as A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

What does AUB mean? ›

Abnormal uterine bleeding (AUB) is bleeding from the uterus that is longer than usual or that occurs at an irregular time. Bleeding may be heavier or lighter than usual and occur often or randomly.

How do you write A∩ B? ›

The symbol for the intersection of sets is "∩''. For any two sets A and B, the intersection, A ∩ B (read as A intersection B) lists all the elements that are present in both sets (common elements of A and B). For example, if Set A = {1,2,3,4,5} and Set B = {3,4,6,8}, A ∩ B = {3,4}.

What is a ∪ b? ›

Operations on sets

The symbol ∪ is employed to denote the union of two sets. Thus, the set A ∪ B—read “A union B” or “the union of A and B”—is defined as the set that consists of all elements belonging to either set A or set B (or both).

How to find a ∩ b? ›

How Do you Find A ∩ B? A ∩ B can be determined by considering only the elements that are present in both A and B. A ∩ B consists the common elements only.

What is the upside down U in a Venn diagram? ›

Upside down U in venn diagrams is known as “intersection”. It means 'and'. In probability theory A∩B A ∩ B means the intersection of events A and B.

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