# First Order Logic: Truth Value of a statement

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?

• I can't see anything wrong with your reasoning. Are you sure you read/wrote the question and answer correctly? If this is the case, then the textbook is incorrect. Commented Apr 18, 2020 at 6:26
• @user400188 Yeah the question is correct. It might be wrong in the textbook. I'll verify my solution. Thanks for the quick reply. Commented Apr 18, 2020 at 6:39