Number of Relations from Set A to Set B which are not Functions 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%

✖No. of Relations A to B which are not Functions is the number of binary relations R from set A to set B which are not functions.ⓘ Number of Relations from Set A to Set B which are not Functions [N_{Relations not Functions}]

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Number of Relations from Set A to Set B which are not Functions

Formula

`"N"_{"Relations not Functions"} = 2^("n"_{"(A)"}*"n"_{"(B)"})-("n"_{"(B)"})^("n"_{"(A)"})`

Example

`"4032"=2^("3"*"4")-("4")^("3")`

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Number of Relations from Set A to Set B which are not Functions Solution

STEP 0: Pre-Calculation Summary

Formula Used

No. of Relations A to B which are not Functions = 2^(Number of Elements in Set A*Number of Elements in Set B)-(Number of Elements in Set B)^(Number of Elements in Set A)
N_{Relations not Functions} = 2^(n_(A)*n_(B))-(n_(B))^(n_(A))
This formula uses 3 Variables

Variables Used

No. of Relations A to B which are not Functions - No. of Relations A to B which are not Functions is the number of binary relations R from set A to set B which are not functions.
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 not Functions} = 2^(n_(A)*n_(B))-(n_(B))^(n_(A)) --> 2^(3*4)-(4)^(3)

Evaluating ... ...

N_{Relations not Functions} = 4032

STEP 3: Convert Result to Output's Unit

4032 --> No Conversion Required

FINAL ANSWER

4032 <-- No. of Relations A to B which are not Functions

(Calculation completed in 00.004 seconds)

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< 4 Functions Calculators

Number of Relations from Set A to Set B which are not Functions

Go No. of Relations A to B which are not Functions = 2^(Number of Elements in Set A*Number of Elements in Set B)-(Number of Elements in Set B)^(Number of Elements in Set A)

Number of Injective (One to One) Functions from Set A to Set B

Go Number of Injective Functions from A to B = (Number of Elements in Set B!)/((Number of Elements in Set B-Number of Elements in Set A)!)

Number of Functions from Set A to Set B

Go Number of Functions from A to B = (Number of Elements in Set B)^(Number of Elements in Set A)

Number of Bijective Functions from Set A to Set B

Go Number of Bijective Functions from A to B = Number of Elements in Set A!

Number of Relations from Set A to Set B which are not Functions 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.

What is a Function?

A Function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

How to Calculate Number of Relations from Set A to Set B which are not Functions?

Number of Relations from Set A to Set B which are not Functions calculator uses No. of Relations A to B which are not Functions = 2^(Number of Elements in Set A*Number of Elements in Set B)-(Number of Elements in Set B)^(Number of Elements in Set A) to calculate the No. of Relations A to B which are not Functions, The Number of Relations from Set A to Set B which are not Functions formula is defined as the number of binary relations R from set A to set B which are not functions. No. of Relations A to B which are not Functions is denoted by N_{Relations not Functions} symbol.

How to calculate Number of Relations from Set A to Set B which are not Functions using this online calculator? To use this online calculator for Number of Relations from Set A to Set B which are not Functions, 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 which are not Functions calculation can be explained with given input values -> 240 = 2^(3*4)-(4)^(3).

FAQ

What is Number of Relations from Set A to Set B which are not Functions?

The Number of Relations from Set A to Set B which are not Functions formula is defined as the number of binary relations R from set A to set B which are not functions and is represented as N_{Relations not Functions} = 2^(n_(A)*n_(B))-(n_(B))^(n_(A)) or No. of Relations A to B which are not Functions = 2^(Number of Elements in Set A*Number of Elements in Set B)-(Number of Elements in Set 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 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 which are not Functions?

The Number of Relations from Set A to Set B which are not Functions formula is defined as the number of binary relations R from set A to set B which are not functions is calculated using No. of Relations A to B which are not Functions = 2^(Number of Elements in Set A*Number of Elements in Set B)-(Number of Elements in Set B)^(Number of Elements in Set A). To calculate Number of Relations from Set A to Set B which are not Functions, 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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