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Predicate properties

lemonthree

New member
Apr 11, 2016
20
predicate.JPG
I'm not very sure whether a predicate can be neither true or false, and I haven't seen any example so far.

The second choice is false because it is the truth set that is the set of all values which make the predicate true.
A predicate has finite variables, so the third choice is false too.

I believe the truth set of a predicate can be empty, so the last choice is true.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
I agree with your choices, but I find the questions not precise enough. According to Wikipedia, a predicate on a set $X$ is a function from $X$ to $\{\text{true}, \text{false}\}$. With this definition it is not clear what "always" means in question 1 and what it means for a predicate to contain variables in question 3.