Well, I've read them. I know what they all state. But I don't get their application.
For reference, this is what my text lists them as:
Addition - If A=B, then A+C = B+C
Subtraction - If A=B, then A-C = B-C
Multiplication - If A=B, then AB=BC
Division - If A=B and C =/= 0, then A/C = B/C
Substitution - If A=B, then B can be used for A in any circumstance.
Symmetry - AB=BA
Transitive - If A=B and B=C, then A=C
Reflexive - AB=AB
...That said, I don't really get their usage.
Here's the segment on them from a recent test I got back, along with my answers. I missed 13, 14, and 16. My answers are bold, and my comments are italicized.
12. If JK = PQ and PQ = ST, then JK = ST. Transitive.
13. If AB + CD = EF + CD, then AB = EF. Addition. I don't get where I went wrong here.
14. AB = AB. Transitive. This is purely me forgetting about Reflexive, and forgetting whether Transitive was the A=A one or the A=B/B=C:A=C one.
15. If AB = CD, then CD = AB. Symmetric.
16. If AB - CD = EF - CD, then AB = EF. Subtraction. Same song as 13. Not sure where I went wrong.
I got the rest of the test right, except for one problem I just made an easy-to-fix stupid mistake on. So these alone are causing me problems. Help, please?