Question

Prove that if xy > 0, then either x > 0 and y > 0 or x < 0 and y < 0

Answer 1

The rule of product states that:

• $(+) \cdot (+) = (+)$
• $(+) \cdot (-) = (-)$
• $(-) \cdot (+) = (-)$
• $(-) \cdot (-) = (+)$

So, a product is positive if and only if both factors have the same sign, and is negative if only if the factors have opposite sign.