whats ans of this qn and please explain
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
or some x is only the divisor of all y.
now converting it to two place predicate...
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.