In the proof that the sum of rational numbers ab and cd , where a, b, c, and d are integers and b and d are non-zero, is a rational number, name the property that states that ad+bc and bd are integers. Enter 1 for option 1, 2 for option 2, and 3 for option 3.

Answer 1

The property that states that \( ad + bc \) and \( bd \) are integers is typically referred to as the Closure Property of integers under addition and multiplication. However, the combination used here specifically relates to the operations performed on integers. So:

1. If the options relate to common mathematical properties:
   • Closure Property (for both addition and multiplication)
   • Associative Property
   • Commutative Property

Given the context of your question, I would select 1 for Closure Property.