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Number of Antisymmetric Relations on Set A Formula

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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. Check FAQs

N Antisymmetric Relations = 2^{n (A)} \cdot 3^{\frac{n (A) \cdot (n (A) - 1)}{2}}

N_{Antisymmetric Relations} - No. of Antisymmetric Relations on A?n_(A) - Number of Elements in Set A?

Number of Antisymmetric Relations on Set A Example

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Here is how the Number of Antisymmetric Relations on Set A equation looks like with Values.

Here is how the Number of Antisymmetric Relations on Set A equation looks like with Units.

Here is how the Number of Antisymmetric Relations on Set A equation looks like.

216 = 2^{3} \cdot 3^{\frac{3 \cdot (3 - 1)}{2}}

216 = 2^{3} \cdot 3^{\frac{3 \cdot (3 - 1)}{2}}

216 = 2^{3} \cdot 3^{\frac{3 \cdot (3 - 1)}{2}}

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Number of Antisymmetric Relations on Set A Solution

Follow our step by step solution on how to calculate Number of Antisymmetric Relations on Set A?

FIRST Step Consider the formula

N Antisymmetric Relations = 2^{n (A)} \cdot 3^{\frac{n (A) \cdot (n (A) - 1)}{2}}

Next Step Substitute values of Variables

∴

N Antisymmetric Relations = 2^{3} \cdot 3^{\frac{3 \cdot (3 - 1)}{2}}

Next Step Prepare to Evaluate

∴

N Antisymmetric Relations = 2^{3} \cdot 3^{\frac{3 \cdot (3 - 1)}{2}}

LAST Step Evaluate

∴

N Antisymmetric Relations = 216

Number of Antisymmetric Relations on Set A Formula Elements

Variables

No. of Antisymmetric Relations on A

Symbol: N_{Antisymmetric Relations}

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find No. of Antisymmetric Relations on A

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.

Symbol: n_(A)

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Elements in Set A

Other formulas in Relations category

Go Number of Relations from Set A to Set B

N Relations(A-B) = 2^{n (A) \cdot n (B)}

Go Number of Reflexive Relations on Set A

N Reflexive Relations = 2^{n (A) \cdot (n (A) - 1)}

Go Number of Symmetric Relations on Set A

N Symmetric Relations = 2^{\frac{n (A) \cdot (n (A) + 1)}{2}}

Go Number of Relations on Set A

N Relations(A) = 2^{{n (A)}^{2}}

How to Evaluate Number of Antisymmetric Relations on Set A?

Number of Antisymmetric Relations on Set A evaluator 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 evaluate 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 evaluate Number of Antisymmetric Relations on Set A using this online evaluator? To use this online evaluator for Number of Antisymmetric Relations on Set A, enter Number of Elements in Set A (n_(A)) and hit the calculate button.

FAQs on Number of Antisymmetric Relations on Set A

What is the formula to find Number of Antisymmetric Relations on Set A?

The formula of Number of Antisymmetric Relations on Set A is expressed as 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). Here is an example- 12 = 2^(3)*3^((3*(3-1))/2).

How to calculate Number of Antisymmetric Relations on Set A?

With Number of Elements in Set A (n_(A)) we can find Number of Antisymmetric Relations on Set A using the formula - 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).

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