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Truth Tables help? P | Q | P | (P AND Q) | P -> (P AND Q)?
I don't even know how to start with this table, and every time I do it I get more frustrated and confused. The starting is easier, but then when I get to the (p AND q) part, it doesn't make sense to me, especially the p -> (p AND q). At least with me, it helps when sentences are used, and I even tried that and it didn't make sense. Would p be the same sentence in the p -> (p AND q)? Why would that be so? And also, wouldn't both of p and q need to be the same (let's say the positive standing on the sentence it represents or NOT?) to be true?
So this is the correct answer (the p columns were given to us to use):
p|q|p| (p AND q) | p -> (p AND q)
T|T|T| T | T
T|F|T| F | F
F|T|F| F | Tx
F|F|F| Fx | T
The ones with x next to the letters were the ones I got wrong originally (but are the correct answers on there). What I mostly don't understand is why, if p and q in the first two columns are false, why is the (p AND q) statement false, but in the p -> (p AND q) everything is false, the statement is true?
The other question I was really hoping someone could answer is whether or not the the p 'sentence' would be the same thing in p -> (p AND q). so if p represents 'the cat is wet', and q represents 'you should dry the cat', and saying in the first row, would that read, "If the cat is wet, then the cat is wet and you should dry it"?
I'm trying to explain it but I don't have enough space to do it..
1 Answer
- Anonymous7 years ago
p and q literally means that both p and q are both true.
I read p -> (p and q) as p implies (p and q). The only combination that would make this false is if p was true but (p and q) was false.
Regarding the cat question, yes!