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I have to find the truth values of the given statements in the domain of discourse D = {2,3,4}

  1. p : ∃x ∀y(x²<2y)
  2. q : ∀y ∃x(x=y+1 or 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 Apr 18 '20 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 Apr 18 '20 at 6:39
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What am I missing here ?

That textbooks can be wrong on occasion.

That is all.

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