what is the negation" all cabbages are green

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what is the negation" all cabbages are green

Mathematics
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suppose that "if z is a w-group then z is solvable" is a true statement, you also know that the "z is solvable" is true. can you deduce that "z is a w-group" is true?
i wish i was good a math

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no because for the statement to be true z is a w-group could be true or false
unless there's more to that question...don't you just put a "not" before the adjective?
igbasallote what are you talking about?
in a "if p then q" statement. if "if p" is false the whole statement is true regardless of then p. If they are both true then it is also true. It can only be false if "if p" is true and "then q" is flase.
I can give you an example to clarify if you want
I was answering ur second question by the way
@lgbasollote was answering your first.
and @lgbasallote you were correct
I don't get what lgbasallote was saying
actually let me look at me logic notes to make sure.
The correct answer to your first question is All cabages are not green
Like the car is red. The negation is the car is not red
why isn't it not all cabbages are green
because that implies that some are green
we want to to do a complete opposite
its confusing I know
so u wan't to tell that none of them are green right?
correct
Did you understand what I was saying to your second question
im trying to figure it out now
What class is this? just curious
advanced mathematics
whole class based on proofs basically
induction proofing, contradictions, and now we are at sets theories
I took a class called mathematical logic which involved a bunch of this stuff. Kinda interesting kinda hell
I hate sets
Only class I have ever had to drop cuz i was failing. Sets, relations, and functions.
Let me know if you don't understand my explanation about your second question I can provide an example that would make it clearer. I'm going to move on to other questions
thats pretty much what i am in now, and let me tell you that I have no idea how im going to pass that class
Logic was kinda fun. Sets is hell. I would master definitions. completely understand what a subset is and what real numbers and complex numbers. just master definitions because you can use those in ur proofs. I wish I had done that.
im trying to figure out that example and don't completely get it So P=>Q so if z is a w-group then z is solvable IS TRUE, then "Z is solvable is also true" why s s "Z is a w-group false?
The negation of "all cabbages are green" is "there exists a cabbage which is not green". All is a quantifier.
isn't the negation "all cabbages are not green?"
So @DanielxAK we just had to show that for all to be false one is true?
lets use p and q for your question all the words are confusing me lol. So the question is essentially... If, if p then q is true, then q is true" So its a nested statement?
P-->Q T Premise Q T Prove
I'm not sure I understand what you mean by that. If it was phrased, cabbage is green. Then, the negation would be cabbage is not green. But, you have "all cabbages are green". So, the negation would be "there exists a cabbage which isn't green". The negation of all is one. This might be able to explain it better than I can: http://www.math.cornell.edu/~hubbard/negation.pdf
Good catch Daniels
Your second question @math_proof, I think it is a correct statement. Because "if p" is true, for the statement to be true (which it is by a premise) "then q" must be true. and "if p" is false. Then "then q" is assumed true because it can't be proven otherwise.
You got me inerested now. I dug out my logic notes. Law of Equivalence for Implication and Disjunction (LEID) states IF p-->q is true, THEN not p or q is true
still confused omg
So we are Given that P --> Q is true correct? and we have to prove that Q is true? am I understanding right?
we know that Q is true
so P can be either true of false
so P=>Q, z is a w-group then z is solvable" is a true statement, so P->Q is true and we know Q is true because "Z is solvable" so P can be either True of False? thats what i'm thinking
P->Q T Premise Q T Premise P T Prove Ok I'm on the right page
So I would say the answer is ~P V P
thats based on truth table on logical implication
I agree
so we can't deduce if P is true
I have this cheat sheet that my teacher made us with all the laws of logic that can be used in a proof. If you'd like it i'll email it to you. Just private message me your email. If you are not comfortable with that I guess I could post it on this thread, but I've got warned for stuff like that
I guess we can't for certain
omg thanks so much for that, I actually get it now
No problem. When you jump into sets I will be no help. Like I said earlier for sets proofs I would master definitions because my teacher used a lot of "By def'n..." in her proofs
i never heard of this website, but now that i discovered it is so useful and helpful and for free
how do you give a medal?
oo oki got it

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