Writing Assignment 02

Directions.

1. Read the Learning $\LaTeX{}$ document. If you have trouble finding the command for a math symbol you want to use, try looking in this Short Math Guide for $\LaTeX{}$.
2. Get the template for this assignment (or use your own). Here’s how to do it:
   • Go to www.overleaf.com, and make sure you are logged in.
   • In a new window, go here: https://www.overleaf.com/read/tfgzcczpkpvw#151777
   • Click on the menu icon in the upper-left and select “Copy Project”.
   • When ask for a name, choose something like “Math 110A - WA 02” and click “Copy”.
   • When this completes you will be back in your own workspace (instead of mine).
3. Use $\LaTeX$ to type up your proofs of the Propositions to Prove listed below. Make sure to use complete sentences and appropriate punctuation. Also, make sure to edit for typos.
4. Click on the “Download PDF” button (to the right of the “Recompile” button). Save the file somewhere you can easily find it.
5. Submit the pdf in Canvas for the assignment “Writing 02”.
6. Let me know if you have any questions!

Propositions to Prove.

1. Let $*$ be the binary operation on $\mathbb{R}$ defined by $a*b = 1+ab$. Prove that $*$ is not associative. (See Problem 2.28.)
2. Prove that if $G$ is a group, then $G$ has a unique identity element. (See Theorem 2.37.)
3. Prove that if $G$ is a group, then each $g\in G$ has a inverse. (See Theorem 2.41.)