Thread: Surjections and a true/false statement.

This is a question I have on a test paper:

Is the following statement always true? Justify your answer.

If and are surjections where , then g o f: is a surjection.

(I wrote "g o f" when I mean the "composite function of g and f").

I would say this statement is true because the domain of g is contained in the image of f (which is a necessary criterion for g o f to exist).

The composite function of two surjections is also a surjection.

Both these facts mean that the statement is always true.

I think this is right, I just wanted to see if I had overlooked anything.

Hi,

Take a look at this diagram :

maps onto , maps onto and so, according to you, should map onto . Is that true ?

Edit: That's my 666th post.

Right, i'd say that the statement is false then.

The third point in the set C (the point that is in C but not in B) isn't connected to a point in A and since there will always be a point that is not connected to a point in a.

Therefore it cannot be a surjection.

I think i've got it.

Originally Posted by Showcase_22

The third point in the set C (the point that is in C but not in B) isn't connected to a point in A and since there will always be a point that is not connected to a point in a.

Therefore it cannot be a surjection.

That's it!