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

✖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 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 Injective Functions from A to B is the number of functions where every element of Set A is related to a distinct element of Set B such that, for all a and b in A, if f(a)=f(b), then a=b.ⓘ Number of Injective (One to One) Functions from Set A to Set B [N_{Injective Functions}]

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Formula

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

Formula

`"N"_{"Injective Functions"} = ("n"_{"(B)"}!)/(("n"_{"(B)"}-"n"_{"(A)"})!)`

Example

`"24"=("4"!)/(("4"-"3")!)`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)!)
N_{Injective Functions} = (n_(B)!)/((n_(B)-n_(A))!)
This formula uses 3 Variables

Variables Used

Number of Injective Functions from A to B - Number of Injective Functions from A to B is the number of functions where every element of Set A is related to a distinct element of Set B such that, for all a and b in A, if f(a)=f(b), then a=b.
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.
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 B: 4 --> No Conversion Required
Number of Elements in Set A: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_{Injective Functions} = (n_(B)!)/((n_(B)-n_(A))!) --> (4!)/((4-3)!)

Evaluating ... ...

N_{Injective Functions} = 24

STEP 3: Convert Result to Output's Unit

24 --> No Conversion Required

FINAL ANSWER

24 <-- Number of Injective Functions from A to B

(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 Injective (One to One) Functions from Set A to Set B Formula

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)!)
N_{Injective Functions} = (n_(B)!)/((n_(B)-n_(A))!)

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 Injective (One to One) Functions from Set A to Set B?

Number of Injective (One to One) Functions from Set A to Set B calculator uses 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)!) to calculate the Number of Injective Functions from A to B, Number of Injective (One to One) Functions from Set A to Set B is defined as the number of functions where every element of Set A is related to a distinct element of Set B, which means for all a and b in A, if f(a)=f(b), then a=b, or, equivalently, if a≠b, then f(a)≠f(b), and here the condition is number of elements B should be greater than number of elements of A. Number of Injective Functions from A to B is denoted by N_{Injective Functions} symbol.

How to calculate Number of Injective (One to One) Functions from Set A to Set B using this online calculator? To use this online calculator for Number of Injective (One to One) Functions from Set A to Set B, enter Number of Elements in Set B (n_(B)) & Number of Elements in Set A (n_(A)) and hit the calculate button. Here is how the Number of Injective (One to One) Functions from Set A to Set B calculation can be explained with given input values -> 12 = (4!)/((4-3)!).

FAQ

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

Number of Injective (One to One) Functions from Set A to Set B is defined as the number of functions where every element of Set A is related to a distinct element of Set B, which means for all a and b in A, if f(a)=f(b), then a=b, or, equivalently, if a≠b, then f(a)≠f(b), and here the condition is number of elements B should be greater than number of elements of A and is represented as N_{Injective Functions} = (n_(B)!)/((n_(B)-n_(A))!) or 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 Elements in Set B is the total count of elements present in the given finite set B & Number of Elements in Set A is the total count of elements present in the given finite set A.

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

Number of Injective (One to One) Functions from Set A to Set B is defined as the number of functions where every element of Set A is related to a distinct element of Set B, which means for all a and b in A, if f(a)=f(b), then a=b, or, equivalently, if a≠b, then f(a)≠f(b), and here the condition is number of elements B should be greater than number of elements of A is calculated using 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)!). To calculate Number of Injective (One to One) Functions from Set A to Set B, you need Number of Elements in Set B (n_(B)) & Number of Elements in Set A (n_(A)). With our tool, you need to enter the respective value for Number of Elements in Set B & 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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