Let $Q(x,y)$ be the statement $y = 2x +1$ what are the values of the following. The universe is $Z^+$ {1,2,3,....}.
(a) $\forall x\exists y Q(x,y)$ This is true
(b) $\exists x \forall y Q(x,y)$ This is false.
Let $Q(x,y)$ be the statement $y = 2x +1$ what are the values of the following. The universe is $Z^+$ {1,2,3,....}.
(a) $\forall x\exists y Q(x,y)$ This is true
(b) $\exists x \forall y Q(x,y)$ This is false.
The first is true. You are correct. For the second, truth would imply that 2x+1=1 has a positive integer as a solution, which is false, so you are correct again.