I need practice on proofs.(adsbygoogle = window.adsbygoogle || []).push({});

I understand it and it makes sense completely. I don't even question the statement once I work it out in my head. I just can't write it down.

This is from the text:

Basics Concepts of Mathematics from Elias Zakon - The Trillia Group

It is an online text, so it is not homework or anything. Even though I understand it, I still hate the fact that I can't write the proof out. Most of them I can do reasonably well (in my opinion of course). I still write a proof out, but I still don't like it. I will give my proof along with the question, so you can potentially see my problem.

Problems on the Compositions of Relations

Question #8 i) (page 30)

Let T be the family of all one-to-one maps of a set A onto itself. Prove the following:

i) If [itex]f,g \epsilon T[/itex], then [itex]f \circ g \epsilon T[/itex]

Proof:

By Definition,

[tex] f \circ g = \{x|(\exists z) z \epsilon D'_g , z \epsilon D_f \}[/tex]

Note: [itex]\{x,z} \epsilon A[/itex]

This implies that f is creating a variable that is in A and g is taking that variable and creating another (equal or not is irrelevant) variable that is in A.

Since, we are starting with a variable in A and ending with a variable in A, [itex]f \circ g[/itex] satisfies the needs to be an element in T.

*They mention T is a group, which I know nothing about. It is irrelevant to the question.

Note: I know this is a bad proof because it barely clearly states anything. Because I'm learning on my own and because the book doesn't supply enough proofs or any answers to questions, I'm very rusty in this area. My definition for the composition is probably wrong on top of that.

Any help?

I'd post more questions, but let's just start with this one.

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