Question

Suppose I know that [(P implies ~A) and (P implies B) and (P implies C)] is impossible. Does this means that the following statement is true: [(P implies A) and (P implies B) and (P implies C)]?

Any help is greatly appreciated!!!

Answer 1

im pretty sure it means that anything different to the original statement could be true

so although it is possible for [(P implies A) and (P implies B) and (P implies C)] to be true
for example we could also create the statement

[(P implies ~A) and (P implies ~B) and (P implies C)]

im not 100% as logic isnt my strong point

Answer 2

Thanks for your answer...yup, it is the same doubt I have. I don't really know what it means to contradict the original statement...

Answer 3

i have to go, but try this:
colour in the areas implied by P in your first statement, and then colour in the second statement on a new diagram




like i said, i think the answer to your question is that the second statement is not necessarily true if the first is false

Answer 4

Suppose I know that [(P implies ~A)
Does this means that the following statement is true: [(P implies A) ?
as experimentX said this part here is a dead givaweway

Answer 5

how cam P imply both A and ~A ?

Answer 6

can*

Answer 7

you make that statement that is false, that is obviously false.

Answer 8

ok. here I got lost. First, if we know that P implies ~A is true then, it can be true that P implies A, since P true and ~A true implies that P true and A true is false. However, I still don't see what does the impossibility of having my first statement true really means...any help out there?

Answer 9

you may be right that P can imply both A and ~A, but the question asks
" Does this mean that the following statement is true?"
not "Is it \(possible\) for the following statement to be true?"

Answer 10

I actually think that P cannot imply both A and ~A
I think that is a contradiction
but even if it wasn't, the answer to your questions would still be "no".

Answer 11

ok...so the question becomes what does this really implies?

Answer 12

yes, I would take "means" to be interpreted as "implies" rather than "allows for the possibility that"

Answer 13

but either way I'm quite sure that\[P\implies A\wedge\neg A\]is impossible
that is like saying\[x+1=2\implies x=1\text{ and } x\neq1\]nonsense

Answer 14

I agree with you in that P cannot imply both A and not ~A...that is impossible

Answer 15

so anyway you slice it the statement is false

Answer 16

still thinking about the original question though

Answer 17

The only important part of the original Q is
"Suppose I know that [(P implies ~A)...Does this means that the following statement is true: [(P implies A)... ?"
the rest is the same, so all that part is obviously true
the only part to focus on is the parts that area different

Answer 18

parts that are*

Answer 19

the above could be stated as\[x+1=2\implies x\neq2\]does that mean that\[x+1=2\implies x=2\]?
pretty obviously false

Answer 20

yup...so here is the true question I had in mind: i want to show, using proof by contradiction, that (P implies A) and (P implies B) and (P implies C), what do I need to show?

Answer 21

meaning, what type of contradiction I need to create?

Answer 22

you want to prove that (P implies A) and (P implies B) and (P implies C)
given what assumption?

Answer 23

if your assumption is
(P implies ~A) and (P implies B) and (P implies C)
then proof by contradiction is pretty simple:

let (P implies ~A) and (P implies B) and (P implies C)
assume that (P implies A) and (P implies B) and (P implies C)
this implies that (P implies A and ~A)
thus, a contradiction