DM

Question

$P\left ( x,y \right )\Rightarrow x+y=10$

State true/false
1.$\exists x\, \forall y \, \, P\left ( x,y \right )$.

2.$\forall y\, \exists x\, \, P\left ( x,y \right )$

if im wrong plz correct me.......

Answer 1

In Statement 1 value of x should be constant for every y and it should be independent of inner variable which is FALSE here.
x=10-y for every y value there is no fixed x which can satisfy every time this condition.

In Statement 2 value of x keeps on changing for every y here.
x=10-y for any value of y we get some x for which it is TRUE.
we can observe that Statement 1 is more stricter then statement 2.