Truth values of nested quantifiers

[nicnicman]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

This problem doesn't make sense to me. 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.

 

[aralbrec]

It's a typo. Two quantifiers in a row on the same variable is the same as one. It's a bit like Porky Pig "There is a.. There is a... I say, there is an x..."