Final answer:
The given statement claims the existence of at least one real number X that, when multiplied by any Y, results in zero, which is false unless X is specifically the number 0. For any other number, this statement does not hold true, as non-zero numbers multiplied by others will not necessarily give zero.
Step-by-step explanation:
The student's statement P(X,Y) is a formal mathematical claim that reads "There exists an X in the real numbers such that for all Y in the real numbers, XY equals zero." The general claim suggests there is at least one real number X that when multiplied by any real number Y will yield the product zero. This is essentially claiming the existence of a number which is the additive identity for multiplication.
However, if we consider the basic properties of real numbers and multiplication, we know that the only way for a product to be zero is if at least one of the factors is zero. Therefore, the statement is actually false for any X other than zero. If X were not zero, there would not be a universal guarantee that XY=0 for every real number Y. Therefore, the only way this statement can be true is if X is specifically 0, which is the multiplicative absorptive element (anything times zero is zero).
Thus, the statement can be corrected as "There exists an X=0 in the real numbers such that for all Y in the real numbers, XY equals zero." This particular version is true since zero multiplied by any real number is indeed zero.