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Consider a composite $f \circ g(x) = f(g(x))$ of two maps $X \xrightarrow{g} Y \xrightarrow{f} Z$. If $f$ is injective and $g$ is surjective, what is the results of the composition $f \circ g$? [or DNE if it does not always have one of these properties]

Similarly, bijective and surjective, AND bijective and injective?

Thank you!

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closed as off-topic by Bookend, Dan Rust, Hakim, Cookie, studiosus Jul 4 '14 at 1:31

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Bookend, Dan Rust, Hakim, Cookie, studiosus
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What's the definition of each? Just trying to see if you know what each mean. – Amateur Math Guy Feb 23 '13 at 18:54
why did you tag it with number theory? – Dominic Michaelis Feb 23 '13 at 18:56
Welcome to MSE. Please note that LaTeX is the preferred way to write Maths here. Take a look at the editing I did on your question to see some details. Also, one expects to see some kind of progress you have done on your questions. Have you tried constructing examples? – Andreas Caranti Feb 23 '13 at 19:00

A hint on your first question. Try and take $X = Z = \{1, 2\}$ and $Y = \{3\}$.

For your other questions, try some examples, and then decide whether you want to prove something.

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