Question

what is the negation" all cabbages are green

Answer 1

be more specific

Answer 2

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?

Answer 3

i wish i was good a math

Answer 4

no because for the statement to be true z is a w-group could be true or false

Answer 5

unless there's more to that question...don't you just put a "not" before the adjective?

Answer 6

igbasallote what are you talking about?

Answer 7

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.

Answer 8

I can give you an example to clarify if you want

Answer 9

I was answering ur second question by the way

Answer 10

@lgbasollote was answering your first.

Answer 11

and @lgbasallote you were correct

Answer 12

I don't get what lgbasallote was saying

Answer 13

actually let me look at me logic notes to make sure.

Answer 14

The correct answer to your first question is All cabages are not green

Answer 15

Like the car is red. The negation is the car is not red

Answer 16

why isn't it not all cabbages are green

Answer 17

because that implies that some are green

Answer 18

we want to to do a complete opposite

Answer 19

its confusing I know

Answer 20

so u wan't to tell that none of them are green right?

Answer 21

correct

Answer 22

Did you understand what I was saying to your second question

Answer 23

im trying to figure it out now

Answer 24

What class is this? just curious

Answer 25

advanced mathematics

Answer 26

whole class based on proofs basically

Answer 27

induction proofing, contradictions, and now we are at sets theories

Answer 28

I took a class called mathematical logic which involved a bunch of this stuff. Kinda interesting kinda hell

Answer 29

I hate sets

Answer 30

Only class I have ever had to drop cuz i was failing. Sets, relations, and functions.

Answer 31

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

Answer 32

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

Answer 33

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.

Answer 34

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?

Answer 35

The negation of "all cabbages are green" is "there exists a cabbage which is not green". All is a quantifier.

Answer 36

isn't the negation "all cabbages are not green?"

Answer 37

So @DanielxAK we just had to show that for all to be false one is true?

Answer 38

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?

Answer 39

P-->Q T Premise
Q T Prove

Answer 40

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

Answer 41

Good catch Daniels

Answer 42

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.

Answer 43

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

Answer 44

still confused omg

Answer 45

So we are Given that P --> Q is true correct? and we have to prove that Q is true? am I understanding right?

Answer 46

we know that Q is true

Answer 47

so P can be either true of false

Answer 48

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

Answer 49

P->Q T Premise
Q T Premise
P T Prove

Ok I'm on the right page

Answer 50

So I would say the answer is ~P V P

Answer 51

thats based on truth table on logical implication

Answer 52

I agree

Answer 53

so we can't deduce if P is true

Answer 54

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

Answer 55

I guess we can't for certain

Answer 56

omg thanks so much for that, I actually get it now

Answer 57

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

Answer 58

i never heard of this website, but now that i discovered it is so useful and helpful and for free

Answer 59

how do you give a medal?

Answer 60

oo oki got it