Logick!

Hello, friends!

I've been studying a lot lately here in UP Mindanao and these are what I have learned from one of my major subjects, CMSC56:

I have learned that "Logic" is a study of reasoning, a study of necessary truth and of systematic methods for clearly expressing & rigorously demonstrating such truths.

Logical operations are modifiers, conjunctions (and), disjunctions (or), conditional (if-then, implication), bi-conditional (if and only if).

...so on and so forth...

Well, I realised CMSC56 may be a headache in some sort, but it is really intellectually stimulating. Well, I wanna share some of my notes on the application of the rules of inferences in logic:

e.g. You are about to leave for school and discovered you don't have your glasses. You have the following true statements:

1. If my glasses are on the kitchen table, then I saw my glasses at breakfast.
2. I was reading newspapers in the living room or I was reading newspapers in the kitchen.
3. If I was reading newspapers in the living room, then my glasses are on the coffee table.
4. I did not saw my glasses at breakfast.
5. If I was reading my book in bed, then my glasses are on the bed table.
6. If I was reading newspapers in the kitchen, then my glasses are on the kitchen table.

Where are the glasses?

-Here is what we did using the rules of inferences:
1.
p->q (statement 1)
~q (statement 4)
∴~p (new statement 7) [rule of Modus Tollens]

2.
s->p (statement 6)
~p (statement 7)
∴~s (new statement 8) [rule of Modus Tollens]

3.
r∨s (statement 2)
~s (statement 8)
∴r (new statement 9) [rule of Disjunctive Syllogism]

4.
r->t (statement 3)
r (statement 9)
∴t (new statement 10) [rule of Modus Ponens]

and Therefore, the glasses are on the coffee table.

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Oh, how wonderful it is to study... if we do study smarter, we apply smarter. :-)


KENNETH

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