• 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)

Your help is greatly appreciated!
• 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 $\forall xy.\,x=y$.