# Truth Values of Nested Qualifiers

1. Oct 28, 2012

### nicnicman

This problem doesn't make sense to me. Here it is:

Let P(x,y) denote the sentence 2x +y = 1
What is the truth value of ∃x∃xP(x,y) where the domain of x, y is the set of all integers.

Doesn't one of the variables need to be a y in ∃x∃xP(x,y)? In other words shouldn't the proposition be ∃x∃yP(x,y) or something similar?

Could this simply be a typo?

Thanks for any suggestions.

2. Oct 28, 2012

### haruspex

Yes, there needs to be a quantifier for y.
My guess is that it ought to say $\forall x\exists y:P(x,y)$, or possibly with the quantifiers swapped (with a very different answer).