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

Question

are integers. Enter 1 for option 1, 2 for option 2, and 3 for option 3.

Option 1: Associative Property

Option 2: Closure Property

Option 3: Commutative Property

Answer 1

The property that states that \( ad + bc \) and \( bd \) are integers in the context of the proof that the sum of rational numbers is a rational number is the Closure Property.

So, the correct answer is:

2