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 2 years ago
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."
 2 years ago
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."

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joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1So we dont have to worry about negative numbers.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0how does that relate?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0by p im referring to p and q by the way something like \(p \rightarrow q\)

farmdawgnation
 2 years ago
Best ResponseYou've already chosen the best response.1The p is the conditional.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0p succeeds the "if" right?

farmdawgnation
 2 years ago
Best ResponseYou've already chosen the best response.1So 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.

farmdawgnation
 2 years ago
Best ResponseYou've already chosen the best response.1That'd be a problem.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1"only if" works like "if" in reverse.

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0...i didn't know that....

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0are there any other phrases that work as if in reverse?

wio
 2 years ago
Best ResponseYou've already chosen the best response.1A 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 \(A\rightarrow B\)

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0ahh just what i needed. what about necessary but not sufficient?

wio
 2 years ago
Best ResponseYou've already chosen the best response.1necessary but not sufficient basically is the same as necessary.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1necessary and sufficient is biconditional.

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0\[(B \rightarrow A) \wedge (\neg A \rightarrow B)\] like that?

wio
 2 years ago
Best ResponseYou've already chosen the best response.1but clouds don't imply rain.

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0the 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

wio
 2 years ago
Best ResponseYou've already chosen the best response.1I mean you could perhaps say \((B\rightarrow A) \wedge \neg (A\rightarrow B)\)

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0the 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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0so any explanations for that?

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0ahh yes. makes sense

wio
 2 years ago
Best ResponseYou've already chosen the best response.1But 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.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0that's why i hate math.....
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