In the proof that the product of ab

Question

and cd
, 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
and b⋅d
? Enter 1 for option 1 and 2 for option 2.

Option 1: They are both imaginary numbers.

Option 2: They are both integers.

(1 point)

Answer 1

The Closure Property in mathematics states that when you perform an operation (in this case, multiplication) on two numbers from a certain set (here, integers), the result of that operation is also in that same set.

Since \( a \), \( b \), \( c \), and \( d \) are all integers, their products \( a \cdot c \) and \( b \cdot d \) must also be integers.

Therefore, the correct answer is:

2 (They are both integers.)