I am tired of phi's and pi's and psi's, so am going to use A and B
My answers for the truth table
A | not A | B | A implies B | Not A and B
T | F | T | T | F
T | F | F | F | F
F | T | T | T | T
F | T | F | T | F
I guess I need to go to bed. Did I mess up somewhere? Let me know.
Diane, your Not A and B should be Not A or B
ReplyDeleteA | Not A | B | A=>B | Not A or B
ReplyDeleteT | F | T | T | T
T | F | F | F | F
F | T | T | T | T
F | T | F | T | T
Thanks, unknown Tom. :)
DeleteNow for the conclusion: A implies B has the same result as Not A or B.
Definitely need to get some sleep. Sundays and Mondays are busy days for me because of some volunteer commitments I have; tonight isn't much better. I hope to post more if I can get a break at work today, but that isn't likely to happen either :)
I don't know how I ended up being "unknown". I am Tom, really old, retired software developer. I am very familiar with how difficult it is to acquire customer needs and translate them to developers.
ReplyDeleteHi Tom - I had the same issue for a bit last week. Once you log in, you'll need to find the Blogger profile that was created for you and change the Display Name from Unknown to (presumably) Tom. Or Hercules. Your call.
DeleteThanks Max
DeleteYou need to create a Google ID, then log in with it. Welcome, old Tom. You would definitely be one of the people I work with.
ReplyDelete"What conclusions can you draw from the above table?"
ReplyDeleteIt seems like this is demonstrating the part of the lecture where he deduced the two cases when the antecedent was false by using the negation. I think.
I need to watch the chunk of the lecture again.
I get the same conclusion as Diane did above. I found this link useful: http://mathworld.wolfram.com/Implies.html
DeleteHere's another good site:
Deletehttp://www.millersville.edu/~bikenaga/math-proof/truth-tables/truth-tables.html
From the mathworld link:
Delete"In classical logic, A=>B is an abbreviation for ¬A v B"
Whoa. While this makes the same truth table, it feels like it's coming at it from a totally different perspective. Interesting... makes me want to check out the use in classical logic. (time willing... :\ )
Maybe a word description is what is wanted.
ReplyDeleteI suggest
The truth/falsity of a conditional is equivalent to the disjunction of a negative antecedent with a consequent
A mathematical version of a synonym? Isn't that what "A=>B is an abbreviation for ¬A v B" comes down to? Could one say the two forms are equivalent, since one implies the other?
ReplyDeleteI like Francis' definition... it's a synonym. When it comes down to it, no need to be more complicated. I like this group! No need to make it harder than it is. And why didn't I think of using A & B! Another simplification. :)
ReplyDeleteAnd my table looked just like Unknown Tom's. Except I was still using the cumbersome phi & psi.