[TechSyndrome]

I was given a question:



Here are my solutions:

https://dl.dropbox.c...%2018.38.08.jpg

Here are my lecturers sample solutions:

https://dl.dropbox.c...20Solutions.png

As you can see, out of the 8 sub-questions, 1-3 and 7-8 of my solutions are identical to my lecturers solutions. However, 4-6 are different/incorrect. I note that he has put "Sample solution" which I interpret as, "this is one way of looking at it". Can anyone confirm whether my way of looking at it is correct/incorrect.

This post has been edited by TechSyndrome: 28 June 2012 - 11:08 AM

[sepp2k]

Your answers for 4-6 are incorrect.

Your answer to 4 says "¬Q -> P". In words that means "Not snowing implies it is freezing" or equivalently "If it is not snowing, it is freezing". Clearly that's not an accurate thing to say and it is not what sentence for says.

It seems to me that you picked "¬Q -> P" rather than "P -> ¬Q" because it matches the order in which the phrases appear in the sentence. But it's important to realize that the order does not matter. Only the meaning matters.

Your answer for 5 is the same as your answer for 7 except for the order. Since <-> is symmetric (i.e. it doesn't matter whether you say "a <-> b" or "b <-> a" - it means the same thing), that means that your answer to 5 is the same as your answer to 7. But do the sentences "That it is below freezing is necessary for it to be snowing" and "That it is below freezing is necessary and sufficient for it to be snowing" really mean the same thing? Since the latter is the former with the addition of "and sufficient", that could only be the case if "sufficient" meant nothing or if it meant the same thing as "necessary". That is not the case.

Specifically does the sentence "That it is below freezing is necessary for it to be snowing" imply that it always snows when it is below freezing? No, it doesn't. But saying "Q <-> P" would imply that. Saying "Q -> P" as the sample solution does only says that it must be below freezing if it's snowing. It doesn't also imply that it must be snowing when it is below freezing. So "Q -> P" matches what the sentence says.

For sentence 6 note that A being sufficient for B means that B will always happen when A happens. So if A happens and B does not happen, that's proof that A is not sufficient for B.