Question

The set {-1, 0, 1} is NOT closed when which operation is considered? addition o multiplication squaring cubing Previous Next >

Answer 1

Addition

Step-by-step explanation:

The set is closed under a specific operation if when we apply the operation to the elements in the set, the result is an element that belongs to the set.

So, if we apply addition to all elements in the set, we get:

-1 + 0 = - 1

-1 + 1 = 0

0 + 1 = 1

-1 + - 1 = - 2

0 + 0 = 0

1 + 1 = 2

Since -2 and 2 don't belong to the set, we can say that the set is not closed under addition.

For multiplication, we get:

-1 x -1 = 1

0 x 0 = 0

1 x 1 = 1

1 x 0 = 0

-1 x 0 = 0

-1 x 1 = -1

So, the product is always a number of the set, -1, 0, or 1. Then, the set is closed under multiplication.