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To determine the truth values for each of these statements, let's analyze them one by one based on the given statement \( Q(x, y) \), defined as " \( x + y = x - y \) ".

### Step 1: Simplify the Condition
The equation \( x + y = x - y \) implies:
\[
x + y = x - y
\

Let Q(x, y) be the statement "x + y = x - y". If the universe of discourse for both variables consists of all integers, what are the truth values?

Determine the truth values of various predicate logic statements based on the condition Q(x, y) where x + y = x - y, given an integer domain for both variables. This problem covers key concepts in predicate logic and quantifiers, suitable for college-level students in discrete mathematics.

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