Question

If (x, y, z) is a solution for a given equation, what can be assumed without loss of generality?

a) x, y, z are prime numbers.
b) x, y, z are composite numbers.
c) x, y, z are coprime integers.
d) x, y, z are even integers.

Answer 1

Without additional context about the given equation, no general assumptions such as the variables being prime, composite, coprime, or even can be made about the solution (x, y, z). The nature of these variables is defined by the equation they satisfy.

Step-by-step explanation:

When the question states that (x, y, z) is a solution for a given equation, it implies that these variables satisfy the equation when their values are substituted into it. There are no general assumptions that can be made about their nature (whether they are prime, composite, coprime, or even) without more specific information about the equation. For example, if we are dealing with a simple linear equation, such as 7y = 6x + 8, choosing values for the independent variable x allows us to solve for the dependent variable y. Similarly, in more complex scenarios where multiple variables are involved, the nature of the solution will be dictated by the requirements of the equation. Therefore, without additional context, we cannot assume a specific nature for the variables x, y, and z.