Final answer:
The statement that if xy = 0, then x = 0 or y = 0 is true, based on the Zero Product Property in mathematics, which applies to all real numbers when dealing with multiplication.
Step-by-step explanation:
The statement 'For every x, y if xy = 0, then x = 0 or y = 0' is true. This is an application of the Zero Product Property, which states that if the product of two numbers is zero, then at least one of the multiplicands must be zero. This fundamental property of multiplication holds true for all real numbers.
For example, if we have a scenario where x*y = 0 and we know that x is not 0, it must be the case that y is equal to 0 to satisfy the equation. Conversely, if y is not 0, then x must be 0 for their product to be zero.
In the context of vectors, the principle is slightly different. While this property reaffirms that vectors with zero magnitude in either the x or y component result in the entire vector being zero, the statement 'Every 2-D vector can be expressed as the product of its x and y-components' is false, as vectors are typically represented as the sum of their components, not the product.