Math Problem Statement

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?

Solution

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)Q(x, y), defined as " x+y=xyx + y = x - y ".

Step 1: Simplify the Condition

The equation x+y=xyx + y = x - y implies: [ x + y = x - y \

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Math Problem Analysis

Mathematical Concepts

Predicate Logic
Quantifiers
Integer Arithmetic

Formulas

x + y = x - y

Theorems

Quantifier Logic

Suitable Grade Level

College-level Discrete Mathematics