Question

letq(x, y) be the statement "x y=x−y." if the do-main for both variables consists of all integers, what arethe truth values

Answer 1

The truth values of the statement 'let q(x, y) be the statement "x × y = x − y."' with integer domain for x and y are mostly false, as multiplication and subtraction of two integers usually produce different results. There are rare exceptions, such as when x is equal to zero, where the statement can be true.

Step-by-step explanation:

To evaluate the truth values of the statement let q(x, y) be the statement "x × y = x − y.", we need to look at the set of all integers as the domain for variables x and y. However, there is an error in the statement because multiplication and subtraction of two integers rarely yield the same result. For the vast majority of integer pairs (x, y), the statement x × y = x − y is false.

For example, let's test a couple of integer pairs:

• If x = 2 and y = 3, then 2 × 3 ≠ 2 − 3 (6 ≠ -1). The statement is false.
• If x = 0 and y is any integer, then 0 × y = 0 − y (0 = 0). In this rare case, the statement is true.

So, the truth value of q(x, y) varies depending on the chosen integers, but it is predominantly false due to the nature of arithmetic operations involved.