Question

if F:S= S is 1-1, where S is a set , then f is onto . Give reason

Answer 1

if S is a finite set

f is 1 to 1

number of elements in range = number of elements in domain = n(S)

and range is a subset of codomain

so range R is subset of S

R=S

f is onto

IF. S is infinite.

a 1 to 1 function need not be onto

example

f :N ~N. by f(x) =x+2

here f is 1 ~1

but not onto