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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?

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    $\begingroup$ 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. $\endgroup$
    – user400188
    Commented Apr 18, 2020 at 6:26
  • $\begingroup$ @user400188 Yeah the question is correct. It might be wrong in the textbook. I'll verify my solution. Thanks for the quick reply. $\endgroup$
    – rochak
    Commented Apr 18, 2020 at 6:39

1 Answer 1

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What am I missing here ?

That textbooks can be wrong on occasion.

That is all.

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