Question

For which operations is the set {–1, 1} closed?



Choose all answers that are correct.



A.


addition


B.


subtraction


C.


multiplication


D.


division

Answer 1

@Nnesha

Answer 2

To help get started, the set {–1, 1} is not closed under addition.
For a set to closed under an operation means that, in this case, if you add any two elements of the set, then you have to get an element of the set as the sum.

Answer 3

Choose 1 and -1 from the set. Add them to get zero. Zero is not in the set. Therefore, the set is not closed under additon.

Answer 4

ok

Answer 5

B and D?

Answer 6

Now, substraction.

If you subtract any two members of the set, will you always get back a member of the set?

You said B so you're thinking yet. Let's see.

Answer 7

kk

Answer 8

I am taking 1 from the set and subtracting it from itself. 1-1 =0 which is not in the set.

Not closed under subtraction.

Answer 9

What about this: multiplication . Closed? What do you think?

Answer 10

YES

Answer 11

Is b and c right

Answer 12

@SolomonZelman

Answer 13

:(

Answer 14

Did you change your mind about the set being closed under multiplication?

Answer 15

Ya

Answer 16

-1 times 1 = -1
1 times 1 = 1
-1 times -1 = 1

Closed under multiplication

Answer 17

That leaves division.

Answer 18

What do you think, closed or not under division?

Answer 19

I dont think it is

Answer 20

Can you give an example of one number of the set divided by another which would give a number not in the set?

Answer 21

1/1=1
1/(-1)=-1

Answer 22

The set appears to be closed under both multiplication and division.

Answer 23

ohhh i get it!

Answer 24

Could You help with another?

Answer 25

Alright, that is good. In making your closed or not closed decision, test some numbers in the set first. Okay?

Answer 26

>>Could You help with another?

Yes. Please post that question in a new thread because this one is so long already.

Answer 27

ook