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.