Question

QUESTION 7

Which of the following gives an example of a set that is closed under multiplication? Choose all that apply.
The product of an even number and an oven number
The product of an odd number and an odd number
The product of a negative number and a negative number
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The product of a perfect cube and a perfect cube

Answer 1

• The product of an even number and an oven number
• The product of an odd number and an odd number
• The product of a perfect cube and a perfect cube

Explanation:

The product of two even numbers will have at least two factors of 2, so will be even: even numbers are closed under multiplication.

The product of two odd numbers will be an even number plus 1, so will be odd: odd numbers are closed under multiplication.

The product of two cubes will be the cube of the product of their cube roots: cubes are closed under multiplication.

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The product of two negative numbers will be positive, so the set of negative numbers is not closed under multiplication.