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Number of Elements in Union of Three Sets A, B and C Calculator

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✖Number of Elements in Set A is the total count of elements present in the given finite set A.ⓘ Number of Elements in Set A [n_(A)]			+10% -10%
✖Number of Elements in Set B is the total count of elements present in the given finite set B.ⓘ Number of Elements in Set B [n_(B)]			+10% -10%
✖Number of Elements in Set C is the total count of elements present in the given finite set C.ⓘ Number of Elements in Set C [n_(C)]			+10% -10%
✖Number of Elements in Intersection of A and B is the total count of common elements present in both of the given finite sets A and B.ⓘ Number of Elements in Intersection of A and B [n_(A∩B)]			+10% -10%
✖Number of Elements in Intersection of B and C is the total count of common elements present in both of the given finite sets B and C.ⓘ Number of Elements in Intersection of B and C [n_(B∩C)]			+10% -10%
✖Number of Elements in Intersection of A and C is the total count of common elements present in both of the given finite sets A and C.ⓘ Number of Elements in Intersection of A and C [n_(A∩C)]			+10% -10%
✖Number of Elements in Intersection of A, B and C is the total count of common elements present in all of the given finite sets A, B and C.ⓘ Number of Elements in Intersection of A, B and C [n_(A∩B∩C)]			+10% -10%

✖Number of Elements in Union of A, B and C is the total count of elements present in at least one of the three given finite sets A, B and C.ⓘ Number of Elements in Union of Three Sets A, B and C [n_(A∪B∪C)]

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Number of Elements in Union of Three Sets A, B and C Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Elements in Union of A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-Number of Elements in Intersection of A and B-Number of Elements in Intersection of B and C-Number of Elements in Intersection of A and C+Number of Elements in Intersection of A, B and C
n_(A∪B∪C) = n_(A)+n_(B)+n_(C)-n_(A∩B)-n_(B∩C)-n_(A∩C)+n_(A∩B∩C)
This formula uses 8 Variables

Variables Used

Number of Elements in Union of A, B and C - Number of Elements in Union of A, B and C is the total count of elements present in at least one of the three given finite sets A, B and C.
Number of Elements in Set A - Number of Elements in Set A is the total count of elements present in the given finite set A.
Number of Elements in Set B - Number of Elements in Set B is the total count of elements present in the given finite set B.
Number of Elements in Set C - Number of Elements in Set C is the total count of elements present in the given finite set C.
Number of Elements in Intersection of A and B - Number of Elements in Intersection of A and B is the total count of common elements present in both of the given finite sets A and B.
Number of Elements in Intersection of B and C - Number of Elements in Intersection of B and C is the total count of common elements present in both of the given finite sets B and C.
Number of Elements in Intersection of A and C - Number of Elements in Intersection of A and C is the total count of common elements present in both of the given finite sets A and C.
Number of Elements in Intersection of A, B and C - Number of Elements in Intersection of A, B and C is the total count of common elements present in all of the given finite sets A, B and C.

STEP 1: Convert Input(s) to Base Unit

Number of Elements in Set A: 10 --> No Conversion Required
Number of Elements in Set B: 15 --> No Conversion Required
Number of Elements in Set C: 20 --> No Conversion Required
Number of Elements in Intersection of A and B: 6 --> No Conversion Required
Number of Elements in Intersection of B and C: 7 --> No Conversion Required
Number of Elements in Intersection of A and C: 8 --> No Conversion Required
Number of Elements in Intersection of A, B and C: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_(A∪B∪C) = n_(A)+n_(B)+n_(C)-n_(A∩B)-n_(B∩C)-n_(A∩C)+n_(A∩B∩C) --> 10+15+20-6-7-8+3

Evaluating ... ...

n_(A∪B∪C) = 27

STEP 3: Convert Result to Output's Unit

27 --> No Conversion Required

FINAL ANSWER

27 <-- Number of Elements in Union of A, B and C

(Calculation completed in 00.004 seconds)

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Number of Elements in Union of Three Sets A, B and C Formula

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What is a Set?

Mathematically a Set is a well defined collection of objects. For example, "the collection of all people in a village" is a Set. But, "the collection of all rich people in a village" is not a Set, because the term 'rich' is not well defined and it is subjective. Hence it is not a Set in Mathematics. The Set theory - branch of Mathematics dealing with the study of Sets and their properties is a fundamental area of basic Mathematics. The Sets which has a finite number of elements are called Finite Sets. If a Set has infinitely many elements but countable, then it is called as Denumerable Set. And if the elements are uncountably many, then it is called an Uncountable Set.

How to Calculate Number of Elements in Union of Three Sets A, B and C?

Number of Elements in Union of Three Sets A, B and C calculator uses Number of Elements in Union of A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-Number of Elements in Intersection of A and B-Number of Elements in Intersection of B and C-Number of Elements in Intersection of A and C+Number of Elements in Intersection of A, B and C to calculate the Number of Elements in Union of A, B and C, The Number of Elements in Union of Three Sets A, B and C formula is defined as the total count of elements present in at least one of the three given finite sets A, B and C. Number of Elements in Union of A, B and C is denoted by n_(A∪B∪C) symbol.

How to calculate Number of Elements in Union of Three Sets A, B and C using this online calculator? To use this online calculator for Number of Elements in Union of Three Sets A, B and C, enter Number of Elements in Set A (n_(A)), Number of Elements in Set B (n_(B)), Number of Elements in Set C (n_(C)), Number of Elements in Intersection of A and B (n_(A∩B)), Number of Elements in Intersection of B and C (n_(B∩C)), Number of Elements in Intersection of A and C (n_(A∩C)) & Number of Elements in Intersection of A, B and C (n_(A∩B∩C)) and hit the calculate button. Here is how the Number of Elements in Union of Three Sets A, B and C calculation can be explained with given input values -> 27 = 10+15+20-6-7-8+3.

FAQ

What is Number of Elements in Union of Three Sets A, B and C?

The Number of Elements in Union of Three Sets A, B and C formula is defined as the total count of elements present in at least one of the three given finite sets A, B and C and is represented as n_(A∪B∪C) = n_(A)+n_(B)+n_(C)-n_(A∩B)-n_(B∩C)-n_(A∩C)+n_(A∩B∩C) or Number of Elements in Union of A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-Number of Elements in Intersection of A and B-Number of Elements in Intersection of B and C-Number of Elements in Intersection of A and C+Number of Elements in Intersection of A, B and C. Number of Elements in Set A is the total count of elements present in the given finite set A, Number of Elements in Set B is the total count of elements present in the given finite set B, Number of Elements in Set C is the total count of elements present in the given finite set C, Number of Elements in Intersection of A and B is the total count of common elements present in both of the given finite sets A and B, Number of Elements in Intersection of B and C is the total count of common elements present in both of the given finite sets B and C, Number of Elements in Intersection of A and C is the total count of common elements present in both of the given finite sets A and C & Number of Elements in Intersection of A, B and C is the total count of common elements present in all of the given finite sets A, B and C.

How to calculate Number of Elements in Union of Three Sets A, B and C?

The Number of Elements in Union of Three Sets A, B and C formula is defined as the total count of elements present in at least one of the three given finite sets A, B and C is calculated using Number of Elements in Union of A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-Number of Elements in Intersection of A and B-Number of Elements in Intersection of B and C-Number of Elements in Intersection of A and C+Number of Elements in Intersection of A, B and C. To calculate Number of Elements in Union of Three Sets A, B and C, you need Number of Elements in Set A (n_(A)), Number of Elements in Set B (n_(B)), Number of Elements in Set C (n_(C)), Number of Elements in Intersection of A and B (n_(A∩B)), Number of Elements in Intersection of B and C (n_(B∩C)), Number of Elements in Intersection of A and C (n_(A∩C)) & Number of Elements in Intersection of A, B and C (n_(A∩B∩C)). With our tool, you need to enter the respective value for Number of Elements in Set A, Number of Elements in Set B, Number of Elements in Set C, Number of Elements in Intersection of A and B, Number of Elements in Intersection of B and C, Number of Elements in Intersection of A and C & Number of Elements in Intersection of A, B and C and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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