anonymous
  • anonymous
what is the negation" all cabbages are green
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
be more specific
anonymous
  • anonymous
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?
anonymous
  • anonymous
i wish i was good a math

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anonymous
  • anonymous
no because for the statement to be true z is a w-group could be true or false
lgbasallote
  • lgbasallote
unless there's more to that question...don't you just put a "not" before the adjective?
anonymous
  • anonymous
igbasallote what are you talking about?
anonymous
  • anonymous
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.
anonymous
  • anonymous
I can give you an example to clarify if you want
anonymous
  • anonymous
I was answering ur second question by the way
anonymous
  • anonymous
@lgbasollote was answering your first.
anonymous
  • anonymous
and @lgbasallote you were correct
anonymous
  • anonymous
I don't get what lgbasallote was saying
anonymous
  • anonymous
actually let me look at me logic notes to make sure.
anonymous
  • anonymous
The correct answer to your first question is All cabages are not green
anonymous
  • anonymous
Like the car is red. The negation is the car is not red
anonymous
  • anonymous
why isn't it not all cabbages are green
anonymous
  • anonymous
because that implies that some are green
anonymous
  • anonymous
we want to to do a complete opposite
anonymous
  • anonymous
its confusing I know
anonymous
  • anonymous
so u wan't to tell that none of them are green right?
anonymous
  • anonymous
correct
anonymous
  • anonymous
Did you understand what I was saying to your second question
anonymous
  • anonymous
im trying to figure it out now
anonymous
  • anonymous
What class is this? just curious
anonymous
  • anonymous
advanced mathematics
anonymous
  • anonymous
whole class based on proofs basically
anonymous
  • anonymous
induction proofing, contradictions, and now we are at sets theories
anonymous
  • anonymous
I took a class called mathematical logic which involved a bunch of this stuff. Kinda interesting kinda hell
anonymous
  • anonymous
I hate sets
anonymous
  • anonymous
Only class I have ever had to drop cuz i was failing. Sets, relations, and functions.
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
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.
anonymous
  • anonymous
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?
anonymous
  • anonymous
The negation of "all cabbages are green" is "there exists a cabbage which is not green". All is a quantifier.
anonymous
  • anonymous
isn't the negation "all cabbages are not green?"
anonymous
  • anonymous
So @DanielxAK we just had to show that for all to be false one is true?
anonymous
  • anonymous
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?
anonymous
  • anonymous
P-->Q T Premise Q T Prove
anonymous
  • anonymous
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
anonymous
  • anonymous
Good catch Daniels
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
still confused omg
anonymous
  • anonymous
So we are Given that P --> Q is true correct? and we have to prove that Q is true? am I understanding right?
anonymous
  • anonymous
we know that Q is true
anonymous
  • anonymous
so P can be either true of false
anonymous
  • anonymous
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
anonymous
  • anonymous
P->Q T Premise Q T Premise P T Prove Ok I'm on the right page
anonymous
  • anonymous
So I would say the answer is ~P V P
anonymous
  • anonymous
thats based on truth table on logical implication
anonymous
  • anonymous
I agree
anonymous
  • anonymous
so we can't deduce if P is true
anonymous
  • anonymous
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
anonymous
  • anonymous
I guess we can't for certain
anonymous
  • anonymous
omg thanks so much for that, I actually get it now
anonymous
  • anonymous
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
anonymous
  • anonymous
i never heard of this website, but now that i discovered it is so useful and helpful and for free
anonymous
  • anonymous
how do you give a medal?
anonymous
  • anonymous
oo oki got it

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