Hi all,

I have a predicate logic assignment due in a couple hours and need help with a theory question.

The question is:

Suppose some sentence of PL is true one every interpretation with a one-member Universe of Discourse. Does it follow that the sentence is quantificationally true? Explain, making sure that your answer proves your position. (ie. show that no other alternative is possible)

Then of course it does not follow. The sentence $\forall x\,x=x$ is true in all one-element interpretations but is not valid.
4. I am sorry, I meant $\forall xy.\,x=y$.