Number of Elements in Exactly One of 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%

✖No. of Elements in Exactly One of the A, B and C is the total count of elements present in exactly one of the given finite sets A, B and C.ⓘ Number of Elements in Exactly One of Sets A, B and C [n_{(Exactly One of A, B, C)}]

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Formula

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Number of Elements in Exactly One of Sets A, B and C

Formula

`"n"_{"(Exactly One of A, B, C)"} = "n"_{"(A)"}+"n"_{"(B)"}+"n"_{"(C)"}-2*"n"_{"(A∩B)"}-2*"n"_{"(B∩C)"}-2*"n"_{"(A∩C)"}+3*"n"_{"(A∩B∩C)"}`

Example

`"12"="10"+"15"+"20"-2*"6"-2*"7"-2*"8"+3*"3"`

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Number of Elements in Exactly One of Sets A, B and C Solution

STEP 0: Pre-Calculation Summary

Formula Used

No. of Elements in Exactly One of the A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-2*Number of Elements in Intersection of A and B-2*Number of Elements in Intersection of B and C-2*Number of Elements in Intersection of A and C+3*Number of Elements in Intersection of A, B and C
n_{(Exactly One of A, B, C)} = n_(A)+n_(B)+n_(C)-2*n_(A∩B)-2*n_(B∩C)-2*n_(A∩C)+3*n_(A∩B∩C)
This formula uses 8 Variables

Variables Used

No. of Elements in Exactly One of the A, B and C - No. of Elements in Exactly One of the A, B and C is the total count of elements present in exactly one of the 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_{(Exactly One of A, B, C)} = n_(A)+n_(B)+n_(C)-2*n_(A∩B)-2*n_(B∩C)-2*n_(A∩C)+3*n_(A∩B∩C) --> 10+15+20-2*6-2*7-2*8+3*3

Evaluating ... ...

n_{(Exactly One of A, B, C)} = 12

STEP 3: Convert Result to Output's Unit

12 --> No Conversion Required

FINAL ANSWER

12 <-- No. of Elements in Exactly One of the A, B and C

(Calculation completed in 00.004 seconds)

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< 14 Sets Calculators

Number of Elements in Exactly One of Sets A, B and C

Go No. of Elements in Exactly One of the A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-2*Number of Elements in Intersection of A and B-2*Number of Elements in Intersection of B and C-2*Number of Elements in Intersection of A and C+3*Number of Elements in Intersection of A, B and C

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

Go 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 Exactly Two of Sets A, B and C

Go No. of Elements in Exactly Two of the A, B and 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-3*Number of Elements in Intersection of A, B and C

Number of Elements in Symmetric Difference of Two Sets A and B given n(A) and n(B)

Go No. of Elements in Symmetric Difference of A and B = Number of Elements in Set A+Number of Elements in Set B-2*Number of Elements in Intersection of A and B

Number of Elements in Intersection of Two Sets A and B

Go Number of Elements in Intersection of A and B = Number of Elements in Set A+Number of Elements in Set B-Number of Elements in Union of A and B

Number of Elements in Union of Two Sets A and B

Go Number of Elements in Union of A and B = Number of Elements in Set A+Number of Elements in Set B-Number of Elements in Intersection of A and B

Number of Elements in Set A

Go Number of Elements in Set A = Number of Elements in Union of A and B+Number of Elements in Intersection of A and B-Number of Elements in Set B

Number of Elements in Set B

Go Number of Elements in Set B = Number of Elements in Union of A and B+Number of Elements in Intersection of A and B-Number of Elements in Set A

Number of Elements in Symmetric Difference of Two Sets A and B

Go No. of Elements in Symmetric Difference of A and B = Number of Elements in Union of A and B-Number of Elements in Intersection of A and B

Number of Elements in Complement of Set A

Go Number of Elements in Complement of Set A = Number of Elements in Universal Set-Number of Elements in Set A

Number of Elements in Symmetric Difference of Two Sets A and B given n(A-B) and n(B-A)

Go No. of Elements in Symmetric Difference of A and B = Number of Elements in A-B+Number of Elements in B-A

Number of Elements in Difference of Two Sets A and B

Go Number of Elements in A-B = Number of Elements in Set A-Number of Elements in Intersection of A and B

Number of Elements in Union of Two Disjoint Sets A and B

Go Number of Elements in Union of A and B = Number of Elements in Set A+Number of Elements in Set B

Number of Elements in Power Set of Set A

Go Number of Elements in Power Set of A = 2^(Number of Elements in Set A)

Number of Elements in Exactly One of Sets A, B and C Formula

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 Exactly One of Sets A, B and C?

Number of Elements in Exactly One of Sets A, B and C calculator uses No. of Elements in Exactly One of the A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-2*Number of Elements in Intersection of A and B-2*Number of Elements in Intersection of B and C-2*Number of Elements in Intersection of A and C+3*Number of Elements in Intersection of A, B and C to calculate the No. of Elements in Exactly One of the A, B and C, The Number of Elements in Exactly One of Sets A, B and C formula is defined as the total count of elements present in exactly one of the given finite sets A, B and C. No. of Elements in Exactly One of the A, B and C is denoted by n_{(Exactly One of A, B, C)} symbol.

How to calculate Number of Elements in Exactly One of Sets A, B and C using this online calculator? To use this online calculator for Number of Elements in Exactly One of 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 Exactly One of Sets A, B and C calculation can be explained with given input values -> 12 = 10+15+20-2*6-2*7-2*8+3*3.

FAQ

What is Number of Elements in Exactly One of Sets A, B and C?

The Number of Elements in Exactly One of Sets A, B and C formula is defined as the total count of elements present in exactly one of the given finite sets A, B and C and is represented as n_{(Exactly One of A, B, C)} = n_(A)+n_(B)+n_(C)-2*n_(A∩B)-2*n_(B∩C)-2*n_(A∩C)+3*n_(A∩B∩C) or No. of Elements in Exactly One of the A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-2*Number of Elements in Intersection of A and B-2*Number of Elements in Intersection of B and C-2*Number of Elements in Intersection of A and C+3*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 Exactly One of Sets A, B and C?

The Number of Elements in Exactly One of Sets A, B and C formula is defined as the total count of elements present in exactly one of the given finite sets A, B and C is calculated using No. of Elements in Exactly One of the A, B and C = Number of Elements in Set A+Number of Elements in Set B+Number of Elements in Set C-2*Number of Elements in Intersection of A and B-2*Number of Elements in Intersection of B and C-2*Number of Elements in Intersection of A and C+3*Number of Elements in Intersection of A, B and C. To calculate Number of Elements in Exactly One of 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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