Final answer:
The statement is false as shown by counterexamples. The number 2 raised to the power of an irrational results in an irrational number, but 2 is rational. Similarly, an irrational number raised to a power of 0 results in a rational number.
Step-by-step explanation:
The statement "If x^y is an irrational number, then x or y is also an irrational number" can be considered false through counterexamples. For instance, consider the rational number 2 and the irrational number 2. When we raise 2 to the power of 2, we get 2^2, which is an irrational number. However, the base, 2, is indeed a rational number.
Another example is when we raise an irrational number to an integer power. The irrational number e raised to the power of 0, e^0, equals 1, which is rational. This disproves the argument because the exponent is a rational number, 0, while the result is also rational.