• Mar 22nd 2010, 12:23 PM
Taher88
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)

• Mar 22nd 2010, 02:54 PM
emakarov
Does "quantificationally true" mean "valid", i.e., "tautology", or "true in every interpretation"? (Have not heard this term before.)

Then of course it does not follow. The sentence $\forall x\,x=x$ is true in all one-element interpretations but is not valid.
• Mar 22nd 2010, 03:04 PM
Taher88
Yes, quantificationally true means valid and that it is a tautology.
I need an example that proves that this is not the case.

How does http://www.mathhelpforum.com/math-he...20883b7f-1.gif prove this?
• Mar 23rd 2010, 12:31 AM
emakarov
I am sorry, I meant $\forall xy.\,x=y$.