Number of Relations on Set A which are both Symmetric and Antisymmetric 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 Symmetric and Antisymmetric Relations on A is the number of binary relations R on a set A which are both symmetric and antisymmetric.ⓘ Number of Relations on Set A which are both Symmetric and Antisymmetric [N_{Symmetric & Antisymmetric}]

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

Formula

`"N"_{"Symmetric & Antisymmetric"} = 2^("n"_{"(A)"})`

Example

`"8"=2^("3")`

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

STEP 0: Pre-Calculation Summary

Formula Used

No. of Symmetric and Antisymmetric Relations on A = 2^(Number of Elements in Set A)
N_{Symmetric & Antisymmetric} = 2^(n_(A))
This formula uses 2 Variables

Variables Used

No. of Symmetric and Antisymmetric Relations on A - No. of Symmetric and Antisymmetric Relations on A is the number of binary relations R on a set A which are both symmetric and antisymmetric.
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_{Symmetric & Antisymmetric} = 2^(n_(A)) --> 2^(3)

Evaluating ... ...

N_{Symmetric & Antisymmetric} = 8

STEP 3: Convert Result to Output's Unit

8 --> No Conversion Required

FINAL ANSWER

8 <-- No. of Symmetric and Antisymmetric Relations on A

(Calculation completed in 00.004 seconds)

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Created by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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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 Relations on Set A which are both Symmetric and Antisymmetric Formula

No. of Symmetric and Antisymmetric Relations on A = 2^(Number of Elements in Set A)
N_{Symmetric & Antisymmetric} = 2^(n_(A))

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.

What are Symmetric and Antisymmetric Relations?

A relation is said to be a Symmetric Relation if one set, A, contains ordered pairs, (x, y) as well as the reverse of these pairs, (y, x). In other words, if (x, y) ∈ R then (y, x) ∈ R for the relation to be symmetric.

A relation is said to be Antisymmetric Relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. In a formal way, relation R is antisymmetric, specifically if for all a and b in A, if R(x, y) with x ≠ y, then R(y, x) must not hold, or, equivalently, if R(x, y) and R(y, x), then x = y.

How to Calculate Number of Relations on Set A which are both Symmetric and Antisymmetric?

Number of Relations on Set A which are both Symmetric and Antisymmetric calculator uses No. of Symmetric and Antisymmetric Relations on A = 2^(Number of Elements in Set A) to calculate the No. of Symmetric and Antisymmetric Relations on A, The Number of Relations on Set A which are both Symmetric and Antisymmetric formula is defined as the number of binary relations R on a set A which are both symmetric and antisymmetric. No. of Symmetric and Antisymmetric Relations on A is denoted by N_{Symmetric & Antisymmetric} symbol.

How to calculate Number of Relations on Set A which are both Symmetric and Antisymmetric using this online calculator? To use this online calculator for Number of Relations on Set A which are both Symmetric and Antisymmetric, enter Number of Elements in Set A (n_(A)) and hit the calculate button. Here is how the Number of Relations on Set A which are both Symmetric and Antisymmetric calculation can be explained with given input values -> 8 = 2^(3).

FAQ

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

The Number of Relations on Set A which are both Symmetric and Antisymmetric formula is defined as the number of binary relations R on a set A which are both symmetric and antisymmetric and is represented as N_{Symmetric & Antisymmetric} = 2^(n_(A)) or No. of Symmetric and Antisymmetric Relations on A = 2^(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.

How to calculate Number of Relations on Set A which are both Symmetric and Antisymmetric?

The Number of Relations on Set A which are both Symmetric and Antisymmetric formula is defined as the number of binary relations R on a set A which are both symmetric and antisymmetric is calculated using No. of Symmetric and Antisymmetric Relations on A = 2^(Number of Elements in Set A). To calculate Number of Relations on Set A which are both Symmetric and Antisymmetric, 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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