Sorry if this question is too elementary than usual for this site, but I'm trying to analyze the logical form of the following statement:
3 is a common divisor of 6, 9, and 15.
I'm not sure how to go about constructing its logical form. I'm assuming I only have to look at its meaning and leaving the superfluous details out. But when I tried constructing it, it didn't feel or sound right, so I tried looking up a solution.
Let T = 3 is a common divisor, S = 3 is a common divisor of 6, N = 3 is a common divisor of 9, F = 3 is a common divisor of 15
This is what I got: [(T $\wedge$ S) $\wedge$ (T $\wedge$ N) $\wedge$ (T $\wedge$ F)]
I'm assuming one of my mistakes was introducing an auxiliary element (i.e T) that shouldn't have been there. This is an exercise in Velleman's How To Prove it, specifically chapter 1, number 2(c). I tried looking up a solution since there wasn't one in the appendix, and I found this. As you can see, my solution seems to be way off.
QUESTION: Is this correct? And if so, what does the solution mean? (i.e what do the terms represent? what does "6 mod 3 = 0" mean?) I'm still in the beginning of the book so I haven't seen/been introduced to some of these terms, and it came as quite a surprise.
Also, you'll have to forgive my LaTeX noobiness. To be fair, I never even heard of it until I came across this site, so I'm still learning. Feel free to edit my question. Any help would be appreciated (regarding the problem, not LaTeX) thank you! =)