Question

The zero product property says that if a product of two real numbers is 0, then one of the numbers must be 0.

Which of the following expresses the zero product property formally using quantifiers and variables?
a.∀ real numbers x and y, if x = 0 and y = 0 then xy = 0.
b.∀ real numbers x and y, if xy = 0 then x = 0 and y = 0.
c.∀ real numbers x and y, if xy = 0 then x = 0 or y = 0.
d.∀ real numbers x and y, if x = 0 or y = 0 then xy = 0.

Answer 1

The formal expression of the Zero Product Property is option c: \( \forall \) real numbers x and y, if xy = 0 then x = 0 or y = 0.

Step-by-step explanation:

The Zero Product Property is critical in solving algebraic equations and can be formally described using quantifiers and variables. This property can be stated as: for any real numbers x and y, if the product xy is 0, then at least one of the numbers must be 0. Therefore, the correct formal expression of the Zero Product Property using quantifiers and variables is option c: \( \forall \) real numbers x and y, if xy = 0 then x = 0 or y = 0. This is because the logical connector 'or' signifies that either x, y, or both could be zero to satisfy the equation xy = 0.