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

Answer 1

Division and Multiplication, right?

Answer 2

@zzr0ck3r
@mathmate
@King.Void.
@SolomonZelman

Answer 3

what does it mean set closed?

Answer 4

A set of elements is closed under an operation if, when you apply the
operation to elements of the set, you always get another element of
the set.

Answer 5

It's either A and D or all of them. I'm not sure

Answer 6

ok let us go through them

A) Is there a way to add two elements from the set and not get an element in the set?

Answer 7

Oh wait it can't be division because you can't divide by 0.....

Answer 8

not addition because 1+1 = 2 is not in the set

Answer 9

yes -1 + 1 = 0

Answer 10

right?

Answer 11

while `-1 + 1 = 0` is true, the fact that `1+1=2` means that you can take the elements `1` and `1` (repeat selections are possible), add them up, and get a number that is NOT in the set. So this set is NOT closed under addition

Answer 12

0 x -1 = 0
0 x 1 = 0
1 - 1 = 0
So, is it multiplication and subtraction?

Answer 13

make a 3x3 table

3 rows for the elements -1,0,1
3 columns for the elements -1,0,1

Answer 14

Now let's say we will use the subtraction operation

to fill out the table, we subtract the value on the left from the value up top

eg: -1 minus -1 = -1+1 = 0 and this goes in the first row, first column

the rest of the table is filled out the same way