Logic Problem!

[Kuciwalker]

Originally posted by KrazyHorse
My ranking of you was obviously justified.

I'm pretty sure you got Krill wrong though.

[Provost Harrison]

Originally posted by Oncle Boris
P: Everyday this week I have $10 in my pocket

But it doesn't say that, it says if I have $10 in my pocket.

[Fake Boris]

re: KH

At first glance, it could appear that the 'every day this week' only applies to the first statement, and that the conditioned meant something like "I will eat lunch at KFC [at some later time]", in which case the answer is E.

[Fake Boris]

Originally posted by Provost Harrison


But it doesn't say that, it says if I have $10 in my pocket.

No, PH. The 'if...then' is an operator.

[Provost Harrison]

That is not in dispute, but the problem is you need to know the condition of one to know the other on any given day.

[Fake Boris]

You're not making any sense...

[Provost Harrison]

I've explained it earlier - I'm not rehashing it.

[Fake Boris]

If you've never done any formal logic, I can understand your confusion. But if you actually have, I'm worried.

[Provost Harrison]

I've never done any, but from my interpretation of the question, that is what it is saying...

[Fake Boris]

OK, that's what I thought.

KH would probably explain it better, but since he's obviously intent on being an ass, I'll tell you what's wrong.

The question gives you the following information: that "Every day this week, if I have $10 in my pocket, then I will eat lunch at KFC" is a false statement.

Don't bother with "real-life" thinking. This is formal. You're looking for something you can assuredly infer from this information.

The sentence can be decomposed in two basic statements: P: "every day this week I have $10 in my pocket" and Q: "every day this week I have lunch at KFC". The "if...then" is an operator, just like AND, OR, etc. This is why it's not part of either P or Q, it's only linking them.

Now that you know that the implication between the two is false, you can infer the truth value of P and Q. What "P then Q is false" means is that you've got P but not Q.
Of all the choices, D is the only one that's necessarily true if Q is false.

[Zkribbler]

Originally posted by Colon™
A very cute employee gave me a free coke at a KFC once. Idiotic as I was, I didn't realise free cokes weren't part of regular service.

Once you figured it out, were you able to find your way back to that same KFC?

[Provost Harrison]

Originally posted by Oncle Boris
OK, that's what I thought.

KH would probably explain it better, but since he's obviously intent on being an ass, I'll tell you what's wrong.

The question gives you the following information: that "Every day this week, if I have $10 in my pocket, then I will eat lunch at KFC" is a false statement.

Don't bother with "real-life" thinking. This is formal. You're looking for something you can assuredly infer from this information.

The sentence can be decomposed in two basic statements: P: "every day this week I have $10 in my pocket" and Q: "every day this week I have lunch at KFC". The "if...then" is an operator, just like AND, OR, etc. This is why it's not part of either P or Q, it's only linking them.

Now that you know that the implication between the two is false, you can infer the truth value of P and Q. What "P then Q is false" means is that you've got P but not Q.
Of all the choices, D is the only one that's necessarily true if Q is false.

It still doesn't make sense how you have made that inference from that information, if this is one of those esoteric types of question...well...

[Kuciwalker]

We know ~(P -> Q). The only way we can know that is if we have a counterexample, that is, if we know P ^ ~Q. D is ~Q.

[Provost Harrison]

Yeah, and that really helped

[Kuciwalker]

Okay, here is the truth table for an individual day:

Let P = "I have $10" and Q = "I eat at KFC."

P | Q | P -> Q
--------------
T | T | T
T | F | F
F | T | T
F | F | T

That is, P -> Q is true as long as ~(P ^ ~Q), that is, as long as we don't have an example of me having $10 but not eating at KFC. For P -> Q to be false, it must be P ^ ~Q at least one day, which means it must be ~Q at least one day, which is D.