Question

For which operations is the set {–1, 0, 1} closed?
Choose all answers that are correct.

A. addition
B. division
C. multiplication
D. subtraction

Can you please explain to me how to do this? The whole test is questions like this so I'd like to know how to solve it myself.

Answer 1

a set is closed under an operation if it's the case that whenever you operate on two elements, the result is also in the set .

Answer 2

Ohhhhh, I think I get it.

So like if I multiply 0 by 1 (both in the number set) it equals 0 so it's closed?

Answer 3

right

Answer 4

what about addition?

Answer 5

the set is not closed under addition, 1 + 1 = 2

Answer 6

but 2 is not in the set

Answer 7

what about division. 1/ 0 is not in the set, so its not closed under division.
what about subtraction -1 - (-1) = -2 , but -2 is not in the set .