This statement is not always true, and we can disprove it by providing a counterexample.

Consider the irrational numbers x = sqrt(2) and y = -sqrt(2). Both x and y are irrational numbers.

However, their sum x + y = sqrt(2) - sqrt(2) = 0, which is a rational number.

And their product xy = sqrt(2) * -sqrt(2) = -2, which is also a rational number.

So, in this case, neither x + y nor xy is irrational. Therefore, the statement “Either x + y or xy is irrational” is not always true.

Question

This statement is not always true, and we can disprove it by providing a counterexample.

Consider the irrational numbers x = sqrt(2) and y = -sqrt(2). Both x and y are irrational numbers.

However, their sum x + y = sqrt(2) - sqrt(2) = 0, which is a rational number.

And their product xy = sqrt(2) * -sqrt(2) = -2, which is also a rational number.

So, in this case, neither x + y nor xy is irrational. Therefore, the statement “Either x + y or xy is irrational” is not always true.

Knowee AI · Accepted Answer

This statement is not always true, and we can disprove it by providing a counterexample.

Consider the irrational numbers x = sqrt(2) and y = -sqrt(2). Both x and y are irrational numbers.

However, their sum x + y = sqrt(2) - sqrt(2) = 0, which is a rational number.

And their product xy = sqrt(2) * -sqrt(2) = -2, which is also a rational number.

So, in this case, neither x + y nor xy is irrational. Therefore, the statement “Either x + y or xy is irrational” is not always true.

Suppose x and y are irrational. Prove or disprove the following statement: “Either x + y or xy is irrational.”