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

STEP 0: Pre-Calculation Summary
Formula Used
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
n(Exactly Two of A, B, C) = n(A∩B)+n(B∩C)+n(A∩C)-3*n(A∩B∩C)
This formula uses 5 Variables
Variables Used
No. of Elements in Exactly Two of the A, B and C - No. of Elements in Exactly Two of the A, B and C is the total count of elements present in exactly two of the given finite sets A, B and 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 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 Two of A, B, C) = n(A∩B)+n(B∩C)+n(A∩C)-3*n(A∩B∩C) --> 6+7+8-3*3
Evaluating ... ...
n(Exactly Two 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 Two of the A, B and C
(Calculation completed in 00.004 seconds)

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

​LaTeX ​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
n(Exactly Two of A, B, C) = n(A∩B)+n(B∩C)+n(A∩C)-3*n(A∩B∩C)

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 Two of Sets A, B and C?

Number of Elements in Exactly Two of Sets A, B and C calculator uses 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 to calculate the No. of Elements in Exactly Two of the A, B and C, The Number of Elements in Exactly Two of Sets A, B and C formula is defined as the total count of elements present in exactly two of the given finite sets A, B and C. No. of Elements in Exactly Two of the A, B and C is denoted by n(Exactly Two of A, B, C) symbol.

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

FAQ

What is Number of Elements in Exactly Two of Sets A, B and C?
The Number of Elements in Exactly Two of Sets A, B and C formula is defined as the total count of elements present in exactly two of the given finite sets A, B and C and is represented as n(Exactly Two of A, B, C) = n(A∩B)+n(B∩C)+n(A∩C)-3*n(A∩B∩C) or 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 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 Two of Sets A, B and C?
The Number of Elements in Exactly Two of Sets A, B and C formula is defined as the total count of elements present in exactly two of the given finite sets A, B and C is calculated using 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. To calculate Number of Elements in Exactly Two of Sets A, B and C, you need 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 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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