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[jagadeesh039]

jagadeesh039

jagadeesh039

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In kamal krithi vasan lec , she was explaining an example.i.e,

if xy=x for all y then x=0;

then she explained the solution like the following

for all x(for all y p(x,y,x)->x=0).. this is the solution which was given by her. where p(x,y,x) is a predicate stating the problem

and she explained we should not write  for all y( for all x p(x,y,x)->x=0) as it is a wrong statement..
I did't get the difference between the two statement i.e wrong and correct statements as she explained.
what is the difference between the above. what happens ,if we interchange universal quantifiers.?
and one more thing is. the solution for the prob look to be wrong in both the statements mentioned above.
I think the solution to be., which is just my thinking , I don't know about the result


there exists x(for all y p(x,y,x)->x=0)
if my result is wrong . why it is wrong? and which one is the correct one.? and how? please clarify my doubts?

jagadeesh.

[sri]

sri

sri

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I'm not sure whether I got the first part of the problem. Since both quantifiers are the same (\forall), it should not matter. Unless I have not understood the problem correctly, that is.

About the second part of the problem, \forall x is correct. We happen to know that there is only one solution that satisfies this problem. But the search space is the set of all possible x that can be fit into the equation.

Hope I have answered the question.

-Sri

[bn pradeep]

bn pradeep

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IMO In the first part , The 2 statements are different
for all y p(x,y,x)->x=0  on the other hand for all x p(x,y,x)-> y = 1 (the identity element)