Solve "Logic" Questions: Is Jed Right?

[icystrike]

Homework Statement

Asked at a press conference whether the new signing, Petermass, would be playing in the big match on Saturday, the Manager replied: “Only if Fredericks isn’t fit.” Three of the journalists present noted the announcement as follows:

Jed wrote: “If Fredericks is fit Petermass won’t be playing.”
Ned wrote: “If Fredericks isn’t fit, Petermass will be playing.”
Ted wrote: “If Petermass doesn’t play it’ll mean Fredericks is fit."

Which of them got the facts right?
[Ans: Jed only]

The Attempt at a Solution

A: Petermass playing
B: Frederick is fit

The press conference suggests: B^C → A
Jed: B → A^C
Ned: B^C → A
Ted: A^C → B

How do I tackle such a question? Suggestions please :(

 

[andrewkirk]

The press conference suggests: B^C → A

No. What the manager said at the press conference was A → B^C, as 'X only if Y' means X→Y.

You've got the right idea. Translate the sentence into symbols. To compare whether two symbolic formulas are the same, you see whether one can be converted into the other using valid rules of inference. A key one in this case is
##(X\to Y)\leftrightarrow ((\neg Y)\to\neg X)##

If you are doing a logic course, they should have given you a list of logical axioms and rules of inference that you can use.

 

[icystrike]

Impressive! I'm not taking any logic course, but I suppose good notations can solve half of any problem.

(A→ ¬B)≡ B → ¬A

"If Petermass will play, Frederick is unfit"

is equivalent to

"If Frederick is fit, Petermass will not play"

Therefore, Jed is right!

Thanks:)

 

[phinds]

I think you're right, but the statement was, I believe not really what the manager probably meant. What he SAID was that if Fredericks isn't fit then Petermass MIGHT play. He left open the possibility that there were other conditions to Petermas's playing than just Fredericks not being fit. I think what he MEANT to say was that if Fredericks isn't fit then Petermass will definitely play. That is, I think he meant to link the two conditions as one being the NOT of the other but he didn't do that because English is imprecise unless you are careful.