ace booklet

Question

whats ans of this qn and please explain 

Comments

tell me please why S1 i not correct

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tell me C is the correct answer or not ??

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no

Answer 1

Here P(x,y) means that x is the divisor of y where x and y are the integers from the universe of discourse..

to make it simple let us say y=5 which is divisible by only 1 ,5.

                                            y=15 divisible by 1,3,5,15

we can say that 

every value of y will be divisible by some values of x..

or some x is only the divisor of all y.

now converting it to two place predicate...

∃_x ∀_y P(x,y) means some x is divisor of all y.

or 

∀_y∃_xP(x,y) means all y is dividend of some x.

which means option B is the correct option (S2 and S3 is correct) 

 

Comments

i do understand the universe is set of all integers, 

what you are doing wrong here is you are finding one y for all x which is wrong, you have to find at least one y for each and every x. there is a difference between  

∀x ∃y P(x,y)  and  ∃y ∀x P(x,y)  

The reason why S1 is false because for x=0 we can't find at least one y if the question would have been ∀x ∃y P(x,y) where x is not 0. Then it would be true. 

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yes i got u i was making a mistake i was taking a different path which was wrong and invalid.  it means that all these values of x must divide some y or atleast one y..

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and 0 cannot divide any  number... so its false..

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yeah bro, although thanks for answering