When I said I loved math, I never claimed to be good at it. That's why after finding out Dr. Bill Myers' Logic class (PL 241) met the BSC math graduation requirements, his class is graced my transcript. However, there's a reason why that class meets the math requirement, and it's actually quite simple: 2/3rds of Logic is math. Oops.

Not to spoil everything for you if you're planning on taking it, but be prepared to solve for validity by constructing 8-line truth tables, shading Venn Diagrams (except there are three circles instead of two and some x's go on lines while others go in between them!) and last and most math-y of all, learning 18 rules of Natural Deduction in Propositional Logic.

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If you like puzzles are aren't afraid to memorize multi-step rules to solve them, well then my friends, Natural Deduction is for you. Ah? Undaunted? Then, let me introduce and teach you the 18 steps and you can start solving for them.

First, let's start by a few very important symbols you need to know:

Name: Horseshoe Symbol: ⊃ Translation: If...then...only if

Name: TildeSymbol: ~ Translation:Not, it is not the case that

Modus Ponens (abbreviated MP) is Latin for "the way that affirms by affirming." In symbolic form, the rule is (with 'p' and 'q' each an individual statement):

p ⊃ q

p

__

q

In good ol' English, that can be translated: (p) If I am a human then (q) I am warm blooded. I am (p) a human. Therefore, I am (q) warm blooded.

Rule 2: Modus Tollens (MT)

In Latin, the translation for this rule is "the way that denies by denying." Here's why it's called that:

p⊃q

~q

___

~p

In English this could be translated: (p) If I am a human then (q) I am warm blooded. I am not (q) warm blooded. Therefore, I am not (p) a human.

Rule 3: Hypothetical Syllogism (HS)

I heard someone say the best way to memorize this is by mentally connecting HS to High School. Here's why:

p⊃q

q⊃s

___

p⊃s

In all-too-familiar English: If (p) Phil tells (q) Quincy and then (q) Quincy tells (s) Sally then ultimately (p) Phil told (s) Sally.

Rule 4: Disjunctive Syllogism (DS)

A quick rule to say the least:

pvq

~p

___

q

In my language: Either I'm a (p) male or (q) female. I'm (~q) not a male. Therefore, I am a (q) female.

Rule 5: De Morgan's Rule (DM)

I'm trying to think of a handy way to memorize this one. Except that the inside of a D is almost circular like a dot, and the inside of an M looks like a wedge, and the apostrophe almost looks like a tilde. Almost, I said.

~(p . q) :: (~p v ~q)

or

~(pvq) :: (~p . ~q)

They key thing to remember about this one is the wedge and dot are interchangeable, and the tilde can either go outside the entire parentheses or next to the p and q. In English this would be:

~ I am not ((p)unfriendly and (q) anti-social. Therefore, I am neither (p) unfriendly or (q) anti-social.

The second line is:

~I am not ((p) unfriendly or (q) anti-social). Therefore, I am (~p) not unfriendly and (~q) anti-social.

Think of "com" and in comma, to remember the only thing that changes is switching what is on the left of the symbol to the right. Com works with wedges and dots.

(pvq) :: (qvp)

or

(p . q) :: (q . p)

In the native tongue:

(p) I am a sentence, and (q) I hate repentance. Therefore, (q) I hate repentance, and (q) I am a sentence.

Or, with a wedge:

(p) I am a wedge or (q) I trimmed a hedge. I.e., (q) I trimmed a hedge or (p) I am a wedge.

Rule 7: Associativity (Assoc):

This one you must remember, only works because all the symbols are associated. A statement must be only all wedges or all dots.

[pv(qvs)] :: [(pvq)vs]

or

[p . (q . r)] :: [(p . q) . r]

Let's do a Gollum Guessing Game! I am either (p) a monkey or (q) a fish or (s) turtle. IT DOES NOT MATTER WHERE THE PARENTHESES GO.

The same with I am a girl (p) and I am straight (q) and I am a Christian (s). ALL ARE TRUE SO IT DOES NOT MATTER WHERE THE PARENTHESES GO.

I told you this was math, didn't I? Doesn't this baby look familiar? (But come to think of it, don't all babies?)

p . (q v r) :: (p . q) v (p . r)

or

p v (q . r) :: (pvq) . (pvr)

Let's not use math in this one.

Instead, I'm opting for an English example:

Example One: (p) I am a girl and (am either (q) a princess or (r) a pauper.). Therefore, (I am a girl and a princess) or (a girl and a pauper).

Example Two: (p) I am a Rapunzel or (am (q) wicked and (r) a witch). Therefore, I am ((p) Rapunzel or (r) wicked) and ((p) Rapunzel or (r) a witch).

This follows the rule "two negatives equal a positive." (Also these tools will not let me unbold this sentence so please forgive me):

p::~~p

I am (p) me which means I am not not (p) me.

Rule 10: Transposition (trans).

I have to remember this one as transgender. This may not be PC, but when was I ever PC?

(p⊃q) :: (~p⊃~q)

If (p) I am a man then (q) I am a woman. Therefore, (~p) if am not a man then (~q) I am not a woman.

Rule 11: Material Implication (Impl)

Doctor Myers, I apologize ahead of time for abbreviating this rule as "imp."

p⊃q :: (~pvq)

(p) "James, if you're always cheeky then (q) you're an imp!" :: (~p) "Either you're not always cheeky, or (q) you're an imp!"

Rule 12: Exportation

I was going to make a joke about aliens and Adobe Premiere, but instead I'm going to explain Exportation with anemia.

[(p . q) ⊃ s] :: [p⊃(q⊃s)]

(p)I am weak and (q) and I am pale if (s) I am anemic.

I.e.,

(p) I am weak if (q) I am pale if (because) (s) I am anemic.