# A Union B Union C - Formula, Venn Diagram, Complement, Examples (2023)

Junction A Junction B Junction Cis a collection of elements belonging to sets A, B, and C. This collection of elements is denoted A U B U C and read as "A union B union C". A U B U C consists of elements contained in A or B or C. The union of three sets A, B, and C can be determined by taking all elements of three sets into a single set and avoiding duplicates. We can also determine the number of elements in A Union B Union C using a formula that ensures common elements are not counted more than once.

In this article, we will examine in detail the concept of A Union B Union C along with its Venn diagram, formula and proof of A U B U C formula using formula for union of two sets. We will also understand the complement A Union B Union C with the help of its Venn diagram and elaborated examples for better understanding.

 1 What is A Union B Union C? 2 A Join B Join C Venn-Diagramm 3 A Union B Union C formula 4 A U B U C Complemento 5 Junction A Junction B Junction C Frequently Asked Questions

## What is A Union B Union C?

A union B union C is defined as the union of three sets A, B, and C consisting of elements belonging to those three sets. How do we know that theunion of setsIt is astop operationand represented by the symbol "U", the union of the three sets A, B and C is denoted by A U B U C, which reads "A union B union C". A U B U C consists of elements unique to A, unique to B, and unique to C; elements common to A and B, B and C, and A and C; and elements common in A, B, and C. In simple terms we can say that the elements in A union B are union C in A or B or C.

## A Join B Join C Venn-Diagramm

Now that we understand the meaning of A U B U C in words, let's look at the Venn diagram A to B to C to understand the concept visually. The Venn diagram shown below highlights the orange shaded area of ​​A U B U C and shows the part covered by A Union B Union C of the universal theorem. As we can see, the union of the sets A, B, C contains elements that are only one of these sets, elements that are common to one of these two sets, and elements that are common to all three intermediate sets.

(Video) Sets: Union, Intersection, Complement ## A Union B Union C formula

Now we understand that every element present in set A or in set B or in set C is present in A U B U C. Before proceeding with the formulas, let's write the symbols used to indicate the number of elements in each set.

• n(A U B U C) = number of elements in A U B U C
• n(A) = number of elements in A
• n(B) = number of elements in B
• n(C) = number of elements in C
• n(A ∩ B) = number of elements that A and B have in common
• n(B ∩ C) = number of elements that B and C have in common
• n(A ∩ C) = number of elements that A and C have in common
• n(A ∩ B ∩ C) = number of elements common in A, B and C.

We can find the number of elements in A Union B Union C using a formula. Now n(A) + n(B) + n(C) gives the total number of elements contained in A, B and C, but common elements are counted more than once. Therefore, to ensure that all elements are counted only once, we subtract the number of common elements in two of these sets from n(A) + n(B) + n(C) and add the number of common elements. in all three sets to get the exact number of elements in A U B U C. Therefore, using the definition of A U B U C and the facts given, we have the following formulas A union B union C:

• UN U B U C = {x: x ∈ A (o) x ∈ B (o) x ∈ C}
• 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)
• P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)
• P(A U B U C) = P(A) + P(B) + P(C) if A, B, and C are mutually exclusive.

### A Junction B Junction C Formeltest

As we know, the number of elements in A Union B Union C is given by the formula n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩) given C ) - n(A ∩ C) + n(A ∩ B ∩ C), we next prove this formula using the formula for the number of elements in theUnion of two sets, that is, n(P U Q) = n(P) + n(Q) - n(P ∩ Q). We will use the following formulas to derive the formula for n(A U B U C):

• n(P ∩ (Q U R)) = n((P ∩ Q) U (P ∩ R))
• n(P U Q) = n(P) + n(Q) - n(P ∩ Q)
• n((P ∩ Q) ∩ (P ∩ R)) = n(P ∩ Q ∩ R)

n(A U B U C) = n (A U (B U C))

(Video) Shade Venn Diagram Two Sets Union Intersection Complements Combinations

= n(A) + n(B U C) - n(A ∩ (B U C))

= n(A) + n(B) + n(C) - n(B ∩ C) - n((A ∩ B) U (A ∩ C))

= n(A) + n(B) + n(C) - n(B ∩ C) - [n(A ∩ B) + n(A ∩ C) - n((A ∩ B) ∩ (A ∩ C ))]

= n(A) + n(B) + n(C) - n(B ∩ C) - n(A ∩ B) - n(A ∩ C) + n((A ∩ B) ∩ (A ∩ C) )

= n(A) + n(B) + n(C) - n(B ∩ C) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)

Hence we prove the formula for the number of elements in A union B union C.

(Video) n(aubuc)=n(a)+n(b)+n(c)-n(a∩b)-n(a∩c)-n(b∩c)+n(a∩b∩c) proof

## A U B U C Complemento

Now that we already know the concept of union A, union B, union C, we will next understand their complement, that is, the complement A, union B, union C, denoted by (A U B U C)' or (A U B U C). will.C. (A U B U C)' consists of elements of the universal set that are not contained in any of the sets A, B and C. In other words, we can also say that A U B U C Complement is equal to the intersection ofadds two setsA, B and C, so (A U B U C)' = A' ∩ B' ∩ C'. The Venn diagram below shows the shaded area indicating the complement of A U B U C. Important notes on A U B U C:

• The set of elements in A U B U C is written as A U B U C = {x : x ∈ A (o) x ∈ B (o) x ∈ C}
• The formula for the number of elements in A U B U C is 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).
• A complement union B Union C consists of elements of the universal set that are not contained in any of the sets A, B, and C.

☛ Related Topics:

• The Intersection B Formula
• finite and infinite sets
• same sentences

## Junction A Junction B Junction C Frequently Asked Questions

### What is A Union B Union C in Math?

A B-union C-union is a collection of elements from the sets A, B, and C. It consists of elements belonging to the three sets A, B, and C. Mathematically, a B-union C-union is denoted A U B U C, where U represents the union of the three sets. A U B U C consists of elements unique to A, unique to B, and unique to C; elements common to A and B, B and C, and A and C; and elements common to A, B and C.

### What is the formula for A Union B Union C?

The formula for A Union B Union C is given by A U B U C = {x : x ∈ A (o) x ∈ B (o) x ∈ C}. Show that the elements in A are union B union C in A or B or C. There are two more formulas for A union B union C, giving the number of elements in A union B union C and the probability of A union B union C given for,

• 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)
• P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)
• P(A U B U C) = P(A) + P(B) + P(C) if A, B, and C are mutually exclusive.

### How do I find a Union B Union C?

We can find A union B union C by combining all elements of sets A, B, and C into a single set and avoiding repetition of elements. Since we know that A U B U C = {x: x ∈ A (o) x ∈ B (o) x ∈ C}, this implies that A union B union C consists of elements contained in either A or B or C .

### What is the probability that A joins B and joins C?

The formula for the probability that A will join B is given by: P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P( B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C). If the sets A, B, and C are mutually exclusive, the formula becomes P(A U B U C) = P(A) + P(B) + P(C).

### What is n(A U B U C)?

n(A U B U C) gives the number of elements in A U B U C. We can find the number of elements in A union B union C by using the formula 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).

(Video) A union (B intersection C) and A intersection (B union C)

### What are the elements of A U B U C?

The elements of A U B U C are the elements that are in one of the three sets A or B or C. These elements can only be contained in one of these sets A, B, C; Elements that are common in each of these two sets; and elements common to the three sets.

## FAQs

### What is the complement of a union b union c? ›

(A U B U C)' consists elements of the universal set which are not in any of the sets A, B, and C. In other words, we can also say that A U B U C Complement is equal to the intersection of complements of the sets A, B and C, that is, (A U B U C)' = A' ∩ B' ∩ C'.

How do you find the union B complement in a Venn diagram? ›

The union of the complement of set A and set B is equal to the difference of the universal set(μ) and the intersection of the two sets (A n B). Further we can express A complement union B, either in roster form or using a Venn diagram. Here we can derive A'UB' = μ - (A n B) = (A n B)'.

What is the answer of a union B complement? ›

Now we know that A union B complement is equal to the intersection of the complement of the set A and the complement of the set B, that is, (A U B)' = A' ∩ B'.

How do you find the complement and B complement? ›

A Intersection B Complement is equal to the union of the complements of the sets A and B. Mathematically, it is written as (A ∩ B)' = A' U B'.

How do you solve complements? ›

The complement of any set is represented as A', B', C' etc. In other words, we can say, if the universal set is (U) and the subset of the universal set (A) is given then the difference of universal set (U) and the subset of the universal set (A) is the complement of the subset, that is A' = U - A.

What does AUB )' mean in Venn diagrams? ›

Union The union of two sets A and B, written A U B, is the combination of the two sets. Intersection The intersection of two sets A and B, written AnB, is the overlap of the two sets.

What does AUB )' mean in math? ›

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.

What is a complement in math? ›

The complement of a set in math is defined as a set of elements in the universal set that is not part of the original set.

What is union vs complement? ›

The union is notated A ⋃ B. The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B. The complement of a set A contains everything that is not in the set A.

What is the rule of complements? ›

Complement ruleThe Complement Rule states that the sum of the probabilities of an event and its complement must equal 1, or for the event A, P(A) + P(A') = 1.

### What are complement numbers examples? ›

The result of inverting the bits in a number is called the one's complement of that number. For example, the one's complement of 0110111 is 1001000. It is called the one's complement because when you add the numbers together, you get all 1's. For example, 0110111 + 1001000 = 1111111.

What is 8's complement example? ›

8's complement of octal number is 7's complement of given number plus 1 to the least significant bit (LSB). For example 8's complement of octal number 320 is (777 - 320) + 1 = 457 + 1 = 460. Please note that maximum digit of octal number system is 7, so addition of 7+1 will be 0 with carry 1.

How do you find 2 complement? ›

Step 1: Write the absolute value of the given number in binary form. Prefix this number with 0 indicate that it is positive. Step 2: Take the complement of each bit by changing zeroes to ones and ones to zero. Step 3: Add 1 to your result.

How do you solve 1's and 2's complement? ›

To get 1's complement of a binary number, simply invert the given number. To get 2's complement of a binary number, simply invert the given number and add 1 to the least significant bit (LSB) of given result.

What does ∩ and ∪ mean in math? ›

∪ The symbol ∪ means union. Given two sets S and T, S ∪ T is used to denote the set {x|x ∈ S or x ∈ T}. For example {1,2,3}∪{3,4,5} = {1,2,3,4,5}. ∩ The symbol ∩ means intersection. Given two sets S and T, S ∩ T is used to denote the set {x|x ∈ S and x ∈ T}.

What is the difference between ∪ and ∩? ›

What is union and intersection of sets? The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

What does A∩B mean in math? ›

The intersection operation is denoted by the symbol ∩. The set A ∩ B—read “A intersection B” or “the intersection of A and B”—is defined as the set composed of all elements that belong to both A and B.

How do you answer the 3 Venn diagram? ›

To solve a Venn diagram with 3 circles, start by entering the number of items in common to all three sets of data. Then enter the remaining number of items in the overlapping region of each pair of sets. Enter the remaining number of items in each individual set. Finally, use any known totals to find missing numbers.

How do you find the complement of a graph? ›

In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G.

What is a complement in 3 sets? ›

Intersection Of Three Sets. Venn Diagrams. More Lessons On Sets. The complement of the set X ∩ Y is the set of elements that are members of the universal set U but not members of X ∩ Y. It is denoted by (X ∩ Y) '.

### What is complement of set A and B? ›

Definition. If A and B are sets, then the relative complement of A in B, also termed the set difference of B and A, is the set of elements in B but not in A.

What does a ∩ B mean 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, and are the 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 AUB in sets example? ›

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.

How do you find A∩ B? ›

It is given as, P(A∩B) = P(A) × P(B), where, P(A) is Probability of an event “A” and P(B) = Probability of an event “B”.

What is complement short answer? ›

noun. something that completes or makes perfect: A good wine is a complement to a good meal. the quantity or amount that completes anything: We now have a full complement of packers. either of two parts or things needed to complete the whole; counterpart.

In grammar, a complement is a word or word group that completes the predicate in a sentence. In contrast to modifiers, which are optional, complements are required to complete the meaning of a sentence or a part of a sentence.

What is the complement of 10? ›

Tens Complement
NumberTens ComplementWhy? Because:
737 + 3 = 10
828 + 2 = 10
919 + 1 = 10
10010 + 0 = 10
7 more rows

What are the two types of complements? ›

Types of Complements
• A subject complement is a word or phrase that modifies the noun or pronoun that acts as the subject in the sentence. ...
• An object complement is a word or phrase that modifies the noun or pronoun that acts as the object in the sentence. ...
• Luke and Lorelai named their daughter Rory. –

How do you find the complement in a sentence? ›

A subject complement is found in the predicate of a sentence (the part of the sentence that contains the verb and makes a statement about the subject). The subject complement follows a linking verb (a verb that expresses a state of being).

What is 1's and 2's complement? ›

1's complement of "0111" is "1000" 1's complement of "1100" is "0011" 2's complement of a binary number is 1, added to the 1's complement of the binary number. In the 2's complement representation of binary numbers, the MSB represents the sign with a '0' used for plus sign and a '1' used for a minus sign.

### What is a complement of 5? ›

If you take the 2's complement of 5 ( 0101 ), you get 1011 which is how you represent -5 .

Is the complement of 15? ›

Trigonometry Examples

The complement of 15° is the angle that when added to 15° forms a right angle (90° ).

What is 9's complement example? ›

9's complement of a decimal number is the subtraction of it's each digits from 9. Like 1's complement, 9's complement is used to subtract a number using addition. For example, let us compute value of “718 – 123” using 9's complement and addition. We first find 9's complement of 718 which is 281.

What are complements of unions and intersections? ›

The union is notated A ⋃ B. The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B. The complement of a set A contains everything that is not in the set A.

What is the probability of a union B complement? ›

So, by recalling De Morgan's law and that for mutually exclusive events the probability of their intersection of zero, we've found that for the two mutually exclusive events 𝐴 and 𝐵, the probability of 𝐴 complement union 𝐵 complement is one.

What is the union of a set A with its complement? ›

i) Complement Laws: The union of a set A and its complement A' gives the universal set U of which, A and A' are a subset. Also, the intersection of a set A and its complement A' gives the empty set ∅.

What is the complement of the universal set? ›

The empty set is defined as the complement of the universal set. That means where Universal set consists of a set of all elements, the empty set contains no elements of the subsets. The empty set is also called a Null set and is denoted by '{}'.

What are complements in Venn diagram? ›

If the union of two mutually exclusive sets is the universal set they are called complementary. The intersection of two complementary sets is the null set, and the union is the universal set, as the following Venn diagram suggests.

What is the complement rule for probability? ›

When one of two disjoint events must occur, the two events are said to be complementary. Since one or the other event must occur, the sum of the probabilities of the two complementary events adds up to 1, or 100 percent of the outcomes of the events.

What is the complement of this probability? ›

The complement of an event is the event not occuring. The probability that Event A will notoccur is denoted by P(A'). The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B).

### What is an example of complement? ›

A complement is something that completes or perfects. Her dress perfectly complements the shade of her eyes. They make a great couple; their personalities are a perfect complement to one another.

What are complements of sets? ›

If U is a universal set and A be any subset of U then the complement of A is the set of all members of the universal set U which are not the elements of A. Alternatively it can be said that the difference of the universal set U and the subset A gives us the complement of set A.

What is difference and complement of sets? ›

Complement and Difference of Sets

The complement of a set A is denoted by A' or Ac and it is the difference of the sets U and A, where U is the universal set. i.e., A' (or) Ac = U - A. This refers to the set of all elements that are in the universal set that are not elements of set A.

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