This is a question I have on a test paper:
(I wrote "g o f" when I mean the "composite function of g and f").Is the following statement always true? Justify your answer.
If and are surjections where , then g o f: is a surjection.
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.
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.