Existence of a Solution for an Equation

There exists an $x$ and there exists a $y$ such that $x + y = 15$. Is this statement true or false?

This problem involves determining the truth value of a mathematical statement about the existence of solutions to an equation. The statement, "There exists an x and there exists a y such that x + y = 15," is a classic example of existential quantification in mathematical logic. Here, the key concept is understanding what it means for there to exist elements that satisfy a given condition.

From a high-level perspective, existential quantifiers are used in logic to express that there is at least one element in a defined domain that makes a specific proposition true. In this problem, you are tasked with analyzing whether a pair of real numbers x and y can be found such that their sum equals 15. This is a foundational concept in logic, relevant to understanding how mathematicians and computer scientists approach proving the existence (or non-existence) of certain objects or solutions within theoretical constructs.

Additionally, the trivial nature of the equation x + y = 15 allows for a straightforward solution—a typical approach to verifying such existential claims involves simply finding one example that satisfies the condition. This problem serves as an introductory exercise in engaging with logical statements and understanding how existential quantification functions in math, providing essential skills that are applied in more complex logical reasoning.