I have to find the truth values of the given statements in the domain of discourse $D = \{2,3,4\}$.
$\text{I}.\ p : \exists x \forall y(x^2 < 2y)$
$\text{II}.\ q : \forall y \exists x (x = y+1 \;\;\lor\;\; x = 2y)$
I know the first one is false because although the given statement is true for $y = 3, 4$ but for $y = 2$ there is no $x$ which makes the statement true.
In the second statement also, it is true for $y = 2, 3$ but false for $y = 4$. So since one element of domain does not satisfy the statement the truth value should be false. But the answer in my textbook says its true.
What am I missing here?