Number of Antisymmetric Relations on Set A Calculator

✖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)]

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✖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 Antisymmetric Relations on Set A [N_{Antisymmetric Relations}]

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Number of Antisymmetric Relations on Set A

Formula

`"N"_{"Antisymmetric Relations"} = 2^("n"_{"(A)"})*3^(("n"_{"(A)"}*("n"_{"(A)"}-1))/2)`

Example

`"216"=2^("3")*3^(("3"*("3"-1))/2)`

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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)
N_{Antisymmetric 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

N_{Antisymmetric Relations} = 2^(n_(A))*3^((n_(A)*(n_(A)-1))/2) --> 2^(3)*3^((3*(3-1))/2)

Evaluating ... ...

N_{Antisymmetric 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 00.020 seconds)

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< 11 Relations Calculators

Number of Antisymmetric Relations on Set A

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)

Number of Relations on Set A which are both Reflexive and Antisymmetric

Go No. of Reflexive and Antisymmetric Relations on A = 3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2)

Number of Relations on Set A which are both Reflexive and Symmetric

Go No. of Reflexive and Symmetric Relations on A = 2^((Number of Elements in Set A*(Number of Elements in Set A-1))/2)

Number of Symmetric Relations on Set A

Go Number of Symmetric Relations on Set A = 2^((Number of Elements in Set A*(Number of Elements in Set A+1))/2)

Number of Non Empty Relations from Set A to Set B

Go Number of Non Empty Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B)-1

Number of Reflexive Relations on Set A

Go Number of Reflexive Relations on Set A = 2^(Number of Elements in Set A*(Number of Elements in Set A-1))

Number of Asymmetric Relations on Set A

Go Number of Asymmetric Relations = 3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2)

Number of Irreflexive Relations on Set A

Go Number of Irreflexive Relations = 2^(Number of Elements in Set A*(Number of Elements in Set A-1))

Number of Relations from Set A to Set B

Go Number of Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B)

Number of Relations on Set A which are both Symmetric and Antisymmetric

Go No. of Symmetric and Antisymmetric Relations on A = 2^(Number of Elements in Set A)

Number of Relations on Set A

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

Number of Antisymmetric Relations on Set A Formula

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 N_{Antisymmetric 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 N_{Antisymmetric 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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