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lgbasallote
Group Title
Logic Question:
A positive integer is prime only if it has no other divisors other than 1 and itself.
Why is the p here "A positive integer is prime" and not "it has no other divisors other than 1 and itself."
 one year ago
 one year ago
lgbasallote Group Title
Logic Question: A positive integer is prime only if it has no other divisors other than 1 and itself. Why is the p here "A positive integer is prime" and not "it has no other divisors other than 1 and itself."
 one year ago
 one year ago

This Question is Closed

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
So we dont have to worry about negative numbers.
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
how does that relate?
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
by p im referring to p and q by the way something like \(p \rightarrow q\)
 one year ago

farmdawgnation Group TitleBest ResponseYou've already chosen the best response.1
The p is the conditional.
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
p succeeds the "if" right?
 one year ago

farmdawgnation Group TitleBest ResponseYou've already chosen the best response.1
So you'd rewrite this as, If positive integer n is prime, it has no other divisors other than 1 and itself. However, you CAN'T say.. If n has no other divisors than 1 and itself, it is a positive integer.
 one year ago

farmdawgnation Group TitleBest ResponseYou've already chosen the best response.1
That'd be a problem.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
"only if" works like "if" in reverse.
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
ah, i misunderstood. I would read that statement as: If a number has no divisors other than one and itself, then it is prime.
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
...i didn't know that....
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
are there any other phrases that work as if in reverse?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
A if B becomes B only if A
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
A is necessary for B means \(B\rightarrow A\). A is sufficient for B means \(A\rightarrow B\). A if B means \(B\rightarrow A\) A only if B means \(A\rightarrow B\)
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
ahh just what i needed. what about necessary but not sufficient?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
necessary but not sufficient basically is the same as necessary.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
necessary and sufficient is biconditional.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
The best thing to do is use 'rain' and 'clouds' and see if it makes sense. Then remember that rain implies clouds.
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
\[(B \rightarrow A) \wedge (\neg A \rightarrow B)\] like that?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
but clouds don't imply rain.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
No, not like that.
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
because i remember something that said necessary but not sufficient and had this solution \[(q \rightarrow (\neg r \wedge \neg p)) \wedge \neg((\neg r \wedge \neg p) \rightarrow q)\]
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
the statement was this: For hiking to be safe, it is necessary but not sufficient that berries be not ripe along the trail and for grizzly bears not to have been seen in the area
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
I mean you could perhaps say \((B\rightarrow A) \wedge \neg (A\rightarrow B)\)
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
the p, q, r are these: p: Grizzly bears have been sean in the area q: hiking is safe r: berries are ripe along the trail
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
so any explanations for that?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Well if \(B\rightarrow A\) means necessary and \(A\rightarrow B\) means sufficient then necessary but not sufficient could be written as \(B\rightarrow A)\wedge \neg (A\rightarrow B\))
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
ahh yes. makes sense
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
But there is a big of an ambiguity for me, because when they say necessary and not sufficient, do they mean necessary but not necessarily sufficient, or necessary and never sufficient.
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
that's why i hate math.....
 one year ago
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