“The product of two negative real numbers is not negative.” Is given by ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))Save & Previous

The statement "The product of two negative real numbers is not negative" is given by "∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))".

This statement is in the language of first-order logic. Here's a step-by-step breakdown:

1. "∀x ∀y" means "for all x and for all y". This indicates that the statement applies to all real numbers x and y.

2. "(x < 0) ∧ (y < 0)" means "x is less than 0 and y is less than 0". This specifies that x and y are both negative real numbers.

3. "→" means "implies". This indicates that if the conditions before the arrow are met, then the condition after the arrow must also be met.

4. "(xy > 0)" means "the product of x and y is greater than 0". This is the condition that must be met if x and y are both negative.

So, the entire statement "∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))" translates to "For all real numbers x and y, if x and y are both negative, then the product of x and y is positive". This is a correct representation of the original statement "The product of two negative real numbers is not negative".