Which books on proof-writing are stuitable for someone engaged in self-study? I want to learn how to read and write proofs. I only have basic pre-calculus skills. As I am preparing for my upcoming calculus 1 course, I wanted to understand questions like

Prove $\left|ab\right|=\left|a\right|\left|b\right|$ for any numbers $a$ and $b$.

These questions pop up in various calculus books and I need to understand them. 
Any book recommendations?

If you're just about to move into Calculus I, you don't need to worry much about the formal logic behind the mathematics. Proofs typically pop up first in a linear algebra or abstract algebra course sophomore or junior year at a university. Real analysis is where you need to worry about proving both integral and differential Calculus, but that's a class that you take after you finish the Calculus sequence anyway. Any facts in a basic single variable Calculus class should be easy to prove with information from your textbook, if you are even required to prove anything at all.
