Number of Relations from Set A to Set B 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)]			+10% -10%
✖Number of Elements in Set B is the total count of elements present in the given finite set B.ⓘ Number of Elements in Set B [n_(B)]			+10% -10%

✖Number of Relations from A to B is the number of ordered pairs (a, b) where a is an element of A and b is an element of B such that a ∈ A and b ∈ B, and all of which are a subset of A × B.ⓘ Number of Relations from Set A to Set B [N_{Relations(A-B)}]

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Formula

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Number of Relations from Set A to Set B

Formula

`"N"_{"Relations(A-B)"} = 2^("n"_{"(A)"}*"n"_{"(B)"})`

Example

`"4096"=2^("3"*"4")`

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Number of Relations from Set A to Set B Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B)
N_{Relations(A-B)} = 2^(n_(A)*n_(B))
This formula uses 3 Variables

Variables Used

Number of Relations from A to B - Number of Relations from A to B is the number of ordered pairs (a, b) where a is an element of A and b is an element of B such that a ∈ A and b ∈ B, and all of which are a subset of A × B.
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.
Number of Elements in Set B - Number of Elements in Set B is the total count of elements present in the given finite set B.

STEP 1: Convert Input(s) to Base Unit

Number of Elements in Set A: 3 --> No Conversion Required
Number of Elements in Set B: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_{Relations(A-B)} = 2^(n_(A)*n_(B)) --> 2^(3*4)

Evaluating ... ...

N_{Relations(A-B)} = 4096

STEP 3: Convert Result to Output's Unit

4096 --> No Conversion Required

FINAL ANSWER

4096 <-- Number of Relations from A to B

(Calculation completed in 00.004 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 Relations from Set A to Set B Formula

Number of Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B)
N_{Relations(A-B)} = 2^(n_(A)*n_(B))

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 Relations from Set A to Set B?

Number of Relations from Set A to Set B calculator uses Number of Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B) to calculate the Number of Relations from A to B, Number of Relations from Set A to Set B formula is defined as the number of ordered pairs (a, b) where a is an element of A and b is an element of B such that a ∈ A and b ∈ B, and all of which are a subset of A × B. Number of Relations from A to B is denoted by N_{Relations(A-B)} symbol.

How to calculate Number of Relations from Set A to Set B using this online calculator? To use this online calculator for Number of Relations from Set A to Set B, enter Number of Elements in Set A (n_(A)) & Number of Elements in Set B (n_(B)) and hit the calculate button. Here is how the Number of Relations from Set A to Set B calculation can be explained with given input values -> 4096 = 2^(3*4).

FAQ

What is Number of Relations from Set A to Set B?

Number of Relations from Set A to Set B formula is defined as the number of ordered pairs (a, b) where a is an element of A and b is an element of B such that a ∈ A and b ∈ B, and all of which are a subset of A × B and is represented as N_{Relations(A-B)} = 2^(n_(A)*n_(B)) or Number of Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B). Number of Elements in Set A is the total count of elements present in the given finite set A & Number of Elements in Set B is the total count of elements present in the given finite set B.

How to calculate Number of Relations from Set A to Set B?

Number of Relations from Set A to Set B formula is defined as the number of ordered pairs (a, b) where a is an element of A and b is an element of B such that a ∈ A and b ∈ B, and all of which are a subset of A × B is calculated using Number of Relations from A to B = 2^(Number of Elements in Set A*Number of Elements in Set B). To calculate Number of Relations from Set A to Set B, you need Number of Elements in Set A (n_(A)) & Number of Elements in Set B (n_(B)). With our tool, you need to enter the respective value for Number of Elements in Set A & Number of Elements in Set B 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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