Compound Quantifier Can any one help me what will be the universe discourse of these two statements?
if both statement has natural numbers or same universe of discourse what will be values, that makes 1st statement true and 2nd to false, of x and y?


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*$\forall x~\exists y~[x < y]$

*$\exists y~\forall x~[x < y]$

 A: The writer needs to specify the "universe of discourse" for the formal propositions to be meaningful.  Without specification we can only say that the second proposition implies the first.
If your question is, give a universe of discourse that makes the first statement true and the second statement false, there are many possibilities. 
As Graham Kemp points out, taking the natural numbers as the "model" (universe of discourse), then the first statement is true (for every number $x$, a larger number $y$ exists) but the second statement is false (no number is larger than all numbers, clearly).
Another such model/universe of discourse is the real numbers with usual ordering.
Note that it is the choice of a "universe of discourse" that makes one or both of these statements true or false, not (as the OP expresses it) "what will be values, that makes 1st statement true and 2nd to false, of x and y?"
The choice of values "of x and y" would make sense if the variables $x,y$ appeared free (unbound by quantifiers) in the formulas.  But they do not.  Both variables are quantified, $x$ by universal quantification and $y$ by existential quantification.  That means that the truth or falsity of these statements depends on the model (that is, the set of values and the predicate $\lt$ defined for that domain), and not upon any choosing of values for $x,y$.
In particular the formula $x\lt y$ can be true or false among natural numbers depending on how we choose values, but the quantified formulas used in the Question are not affected by such choices.
