Question

In the proof that the product of ab 𝑎 𝑏 and cd 𝑐 𝑑 , where a, b, c, and d are integers and b and d are non-zero, what does the Closure Property tell you about the products a⋅c 𝑎 ⋅ 𝑐 and b⋅d 𝑏 ⋅ 𝑑 ? Enter 1 for option 1 and 2 for option 2.

Answer 1

The Closure Property states that for any two integers, their product is also an integer. In the case of your question regarding the products \( a \cdot c \) and \( b \cdot d \), both of which are products of integers, the Closure Property implies that:

1. The product \( a \cdot c \) is an integer.
2. The product \( b \cdot d \) is an integer because both \( b \) and \( d \) are non-zero integers.

Thus, the correct option to enter would be **1**, indicating that the products \( a \cdot c \) and \( b \cdot d \) are integers.