injective map and surjective map?

Question

Set X = {1, 2, 3} and Y = {4, 5, 6, 7}.
Give an example of an injective map from X to Y.
Give an example of a surjective map from Y to X.

Can anyone help out?

function f is said to be surjective if its values span its whole codomain; that is, for every y in the codomain, there is at least one x in the domain such that f(x) = y.

So i do understand your post
4-1
5-2
6-3
7-3

but why are both 6 and 7 mapped to 3?

how does that happen? why is it not
4-1
5-1
6-2
7-3

or
4-1
5-2
6-2
7-2

Answer 1

Injective (X to Y):
f(x)=x+3

Surjective (Y to X):
4-->1
5-->2
6-->3
7-->3


Injective means that for every number in the image set (Y), there is AT MOST (maybe no) 1 number that is sent to it. Thus in my example, the "pre-image" of 4 is 1 (and that is the only pre-image).

Surjective means that every number in the image set is in the image of the domain set. Therefore, in my example 1, 2, and 3 all have pre-images.

Answer 2

injective map:
1-->7
2--> 5
3--> 6

surjetive map:
4-->1
5-->3
6-->2
7-->1

these are just 2 examples,
there are plenty more