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The problem reads:

Let $\text{isFatherOf}(x,y)$ be "$x$ is the father of $y$" and the domain $D = \{\text{all people now living or who have lived}\}$. Find the truth value of the quantified statement $\forall x \, \exists y \, \text{isFatherOf}(x,y)$.

The answer given is "False" but I'm not sure how to come to that answer. Would it be best to write out the statement in an English sentence or use a formulaic method to determine the truth value?

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  • $\begingroup$ Because Not all men become fathers (there are men, with no $y$ of which they are the father); and women never become fathers, hence all women are such that they are not fathers of anyone. $\endgroup$ – amWhy Oct 26 '17 at 15:42
  • $\begingroup$ All that is needed to prove this example is to find one person who is living or once lived, that fathered no one. Then we have that it is not the case that ever person x, there exists/existed someone y, who was fathered by x. Personally, I am a person, now living, for which there is no person y, such $isFatherOf(amWhy, y)$ $\endgroup$ – amWhy Oct 26 '17 at 15:46
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Translating it into English is always a good idea to get some better sense of the statement.

This particular statement translates to 'Everyone is (or was) the father of someone'

I think you can see why this is false.

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