One to One Function

(Injection) #

A function f from set ‘A’ to set ‘B’ is one to one if no two elements in ‘A’ are mapped to some element in ‘B’ Image of every member of domain is distinct. $a\ne b\Rightarrow f(a)\ne f(b)$ or $f(a)=f(b) \Rightarrow a=b$

Property #

If f:A→B is one-to-one, |A|=x and |B|=y, then x≤y

Number of possible one to one functions #

If f:A→B is one-to-one, |A|=x and |B|=y possible functions: y⋅(y-1)⋅(y-2)… x number of times= y!/(y-x)! = $^{y}P_{x}$