Question

Let p(x,y) and q(x,y) are open statements where the domain of both x and y is a real number determining the truth value of p(x,y)_q(x,y) for the given values of x and y:

p(x,y): x² + y² ≥ 0
q(x,y): x * y

Answer 1

The truth value of p(x,y)_q(x,y) for given x and y can be partially evaluated; p(x,y) is always true, but q(x,y) lacks a complete statement, making its truth value indeterminable. Mathematical truths don't necessarily apply to other disciplines, and physics uses probabilistic interpretations like the Born interpretation.

Step-by-step explanation:

To determine the truth value of p(x,y)_q(x,y) for given values of x and y, we must evaluate the open statements p(x,y): x² + y² ≥ 0 and q(x,y): x * y, where x and y are real numbers. The statement p(x,y) is always true since the sum of the squares of any two real numbers is non-negative. The statement q(x,y), however, is incomplete as it does not provide a proposition. With the incomplete statement, we cannot assess its truth value.

Additionally, the discussion about different domains of truth in LibreTexts™ implies that mathematical truths do not always apply to other disciplines such as morals or chemistry. In physics, for example, the Born interpretation is mentioned, which provides a probabilistic interpretation of wave functions in quantum mechanics, suggesting that mathematical equations can represent real-world probabilities.