Question

logic question in post

Answer 1

see the picture
why this is true if we changed the direction of implies?

Answer 2

If it is tru that
For all y there exists an x such that some function P(x,y) is true

this does not imply that
There exists an x so that for All y the function P(x,y) is true

for instance P(x,y) is x>y, then
For all y a value of x can be found such that x>y

but it is not true that
There exists a x such that fo All y, x>y

since there is no such thing as a biggest number

Answer 3

OK thanks a lot man
but this methodology is induction right?

Answer 4

I don't think so

Induction is for example
base case
x = 1, something is true for x = 1
x = n, something is true for x = n
Hence it is true for x = n+1, or for all ix

but you could use that for prove both statements, but I don't see how to apply it to the implication (the combination of those statements, that is)

Answer 5

one more question please
Can explain the same example for its converse?

Answer 6

I don't think you use induction to disprove something
It is usually easier to have a counter example

Answer 7

I don't understand what you mean by its convers,
what should that be?

Answer 8

There exists an x so that for All y the function P(x,y) is true
This implies that all y there exists an x such that some function P(x,y) is true
why this implies? with the same example x>y

Answer 9

@abtster

Answer 10

Well, x>y is not a good example for this, it cannot be the function P
Let me think of a better example
hang on

Answer 11

Hey man i need this example as i can't see the difference between both cases

Answer 12

say P x > - y^2

Answer 13

If there is an x such that for all y P is true
therefore for all y there exists an x such that P is true
Yes I think this is true for all valid functions P

Answer 14

OK why didn't we use the example of x>y !!!

Answer 15

If it were not true, then there would not be any x and the first part would not be true

Answer 16

For that function the first statement is not true
and implications of false statements are not valid (they can be true or untrue, but not based on the first statment

The statement
There is an x such that for all y, x>y is not true
So that function cannot be used as an example

Answer 17

why this statement( all y there exists an x) is true ?

Answer 18

it is only true for functions that work, so not all functions are valid for that statement

Answer 19

I think that is a bit of magic
What is the most first step i would do to understand such statement?

Answer 20

Putting it in words, like we did here, and try to understand the line Don forget any element That's how I do it

Answer 21

Then, try to think of an example if there are any abstract elements, such as a general function like P(x,y)
that might be the hardest bit

Answer 22

OK thank you so much.
I have to work it out. I will take a rest then see it again.

Answer 23

Good luck

Answer 24

@abtster Can you tell me if my understanding is right or not?
Q.If there is an x such that for all y P ---> all y there exists an x such that P.
A. so the equation is x = c (assuming it is true) and if i put any value of y that would give me x and its true.Thus it is valid.
Q.all y there exists an x such that some function P(x,y) ---> There exists an x so that for All y the function P(x,y).
A. the equation is y^0=1=c=x (assuming this is true ) .Thus if i knew x I can't predict Y.
Excuse me,I am loading you (Did I get it or not).

Answer 25

It had to be shown that the first Q is generally untrue.
If you find one example of P that makes it untrue then Q is refuted
Even if you can find an example that makes Q true in that particular example of P, that doesn't make Q true in generally true, it just happened to be true in that particular case

Answer 26

An example of P can also make the thesis Q more clear, but doesn't in itself proof anything, a particular example can only disprove if Q is then false

Answer 27

Maybe there is someone in mathematics who knows more about this subject and can explain it better than me

Answer 28

I got it ,so I shouldn't use any example at the first Q ,but use p(x,y) as a general case.
Thanks man I think I got it now :D