Answers

2016-04-08T13:55:15+05:30
One - one function : A function f : A → B is an injection if distinct elements of A have distinct f images in B . An injection is also called one one function.
f : A → B is an injection  ⇔ a₁ , a₂ ∈ A and a₁ ≠ a₂ implies that f(a₁ ) ≠f( a ₂ )
                                       ⇔a₁ , a₂ ∈ A  and f(a₁ ) = f(a₂ ) = f(a₁ ) implies a₁  = a₂
surjection : A function f : A→B is called a surjection if the range of f is equal to the co-domain of f.A surjection is also called onto.
f : A → B is a surjection ⇔range f = f(A) = B ( c0- domain)
                                     ⇔ B = { f(a) / a∈ A}
                                     ⇔ for every b∈B there exists atleast one a∈A such that f(a) =b
0