Number of Antisymmetric Relations on Set A Solution

STEP 0: Pre-Calculation Summary
Formula Used
No. of Antisymmetric Relations on A = 2^(Number of Elements in Set A)*3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2)
NAntisymmetric Relations = 2^(n(A))*3^((n(A)*(n(A)-1))/2)
This formula uses 2 Variables
Variables Used
No. of Antisymmetric Relations on A - No. of Antisymmetric Relations on A is the number of binary relations R such that, ∀ x and y in A, if (x,y) ∈ R with x ≠ y, then (y,x) ∉ R, or, equivalently, if (x,y) ∈ R and (y, x) ∈ R, then x = y.
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.
STEP 1: Convert Input(s) to Base Unit
Number of Elements in Set A: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
NAntisymmetric Relations = 2^(n(A))*3^((n(A)*(n(A)-1))/2) --> 2^(3)*3^((3*(3-1))/2)
Evaluating ... ...
NAntisymmetric Relations = 216
STEP 3: Convert Result to Output's Unit
216 --> No Conversion Required
FINAL ANSWER
216 <-- No. of Antisymmetric Relations on A
(Calculation completed in 00.004 seconds)

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Number of Antisymmetric Relations on Set A Formula

​LaTeX ​Go
No. of Antisymmetric Relations on A = 2^(Number of Elements in Set A)*3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2)
NAntisymmetric Relations = 2^(n(A))*3^((n(A)*(n(A)-1))/2)

What is a Relation?

A Relation in mathematics are used to describe a connection between the elements of two sets. They help to map the elements of one set (known as the domain) to elements of another set (called the range) such that the resulting ordered pairs are of the form (input, output). It is is a subset of the cartesian product of two sets. Suppose there are two sets given by X and Y. Let x ∈ X (x is an element of set X) and y ∈ Y. Then the cartesian product of X and Y, represented as X × Y, is given by the collection of all possible ordered pairs (x, y). In other words, a relation says that every input will produce one or more outputs.

How to Calculate Number of Antisymmetric Relations on Set A?

Number of Antisymmetric Relations on Set A calculator uses No. of Antisymmetric Relations on A = 2^(Number of Elements in Set A)*3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2) to calculate the No. of Antisymmetric Relations on A, The Number of Antisymmetric Relations on Set A formula is defined as the number of binary relations R on a set A in which there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other, which means for all x and y in A, if (x,y) ∈ R with x ≠ y, then (y,x) ∉ R, or, equivalently, if (x,y) ∈ R and (y, x) ∈ R, then x = y. No. of Antisymmetric Relations on A is denoted by NAntisymmetric Relations symbol.

How to calculate Number of Antisymmetric Relations on Set A using this online calculator? To use this online calculator for Number of Antisymmetric Relations on Set A, enter Number of Elements in Set A (n(A)) and hit the calculate button. Here is how the Number of Antisymmetric Relations on Set A calculation can be explained with given input values -> 12 = 2^(3)*3^((3*(3-1))/2).

FAQ

What is Number of Antisymmetric Relations on Set A?
The Number of Antisymmetric Relations on Set A formula is defined as the number of binary relations R on a set A in which there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other, which means for all x and y in A, if (x,y) ∈ R with x ≠ y, then (y,x) ∉ R, or, equivalently, if (x,y) ∈ R and (y, x) ∈ R, then x = y and is represented as NAntisymmetric Relations = 2^(n(A))*3^((n(A)*(n(A)-1))/2) or No. of Antisymmetric Relations on A = 2^(Number of Elements in Set A)*3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2). Number of Elements in Set A is the total count of elements present in the given finite set A.
How to calculate Number of Antisymmetric Relations on Set A?
The Number of Antisymmetric Relations on Set A formula is defined as the number of binary relations R on a set A in which there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other, which means for all x and y in A, if (x,y) ∈ R with x ≠ y, then (y,x) ∉ R, or, equivalently, if (x,y) ∈ R and (y, x) ∈ R, then x = y is calculated using No. of Antisymmetric Relations on A = 2^(Number of Elements in Set A)*3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2). To calculate Number of Antisymmetric Relations on Set A, you need Number of Elements in Set A (n(A)). With our tool, you need to enter the respective value for Number of Elements in Set A 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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