Never minded math. Forgotten most of it. Took calculus as an elective in undergrad. Also used it in the symbolic logic classes. Cool classes. Take any argument and break it down to variables, then derive truth or falsity from the argument.
P->Q
P
------
Q
It's the basic first argument. If/then conditional.
If Sally goes to school today, she will get ice cream. Sally goes to school is P. Ice cream is Q.
So if some one says Sally goes to school, then we can logically conclude that Sally got Ice Cream. This logically holds truth. However, if Sally got Ice Cream, we can't logically conclude she went to school. This is where people use fallacies.
You can affirm the antecedent but can't boy affirm the consequent. Conversely though, you can deny the consequent and thus would equal truth in denying or negating the antecedent. Ant just means 1st term, cons mean last (pretty much like the sound).
So this whole thing expands into complex arguments that can be solved by propositional logic or propositional calculus.
I used to take people's entire arguments and break them down to variables and then "solve" them. Rush Limbaugh was the funniest. Don't care either way about him, but literally every argument never held logical truth. Basically stuff like that.
The issue is though you can lay out someone's argument formulaicly, they have no idea what you are showing them, and only other logicians understand the language. So dumb people, or untrained/uneducated people think they are right, when math shows they are wrong.
Funny though, we don't teach logic in schools as much. Aristotelian logic is the bedrock of Western culture. Literally, how our minds work, comes from Aristotle. We catalog in the western world, break things down to parts, dissect. Other places of the world don't.
My logic teacher, who I had at least 4 classes with, had a final that was completely in jabber wocky, a language Lewis Carroll created (author of Alice in Wonderland, also famous logician)
All mimsy were the borogoves,
And the mome raths outgrabe
And we had to solve it on whether or not the argument made sense. Harder than any law school final.
P ↔ Q
(S v T) → Q
¬P v (¬T & R)
T → U
Would be solved:
1. P ↔ Q Premise
2. (S v T) → Q Premise
3. ¬P v (¬T & R) Premise
4. (P → Q) & (Q → P) 1 Equiv
5. Q → P 4 Simp
6. (S v T) → P 2,5 HS
7. P → (¬T & R) 3 Impl
8. (S v T) → (¬T & R) 6,7 HS
9. ¬(S v T) v (¬T & R) 8 Impl
10. (¬S & ¬T) v (¬T & R) 9 DM
11. [(¬S & ¬T) v ¬T] & [(¬S & ¬T) v R] 10 Dist
12. (¬S & ¬T) v ¬T 11 Simp
13. ¬T v (¬S & ¬T) 12 Com
14. (¬T v ¬S) & (¬T v ¬T) 13 Dist
15. ¬T v ¬T 14 Simp
16. ¬T 15 Taut
17. ¬T v U 16 Add
18. T → U
