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

The set is {-1,1}
An operation is closed when the operation is operated on \(any\) members of the set will give a result which is within the set.

For example, for the addition operation,
-1+-1 =-2 Not in the set, so the operation is not closed on the given set {-1,1}.

Check with other operations to find the required answer.

Answer 2

huh?

Answer 3

for example, your set is not closed with respect to addition, since:
\(1+(-1)=0\)
and \(0\) doesn't belong to your set

Answer 4

ok, so addition?

Answer 5

so, addition is a wrong option

Answer 6

oh...

Answer 7

multiplucation

Answer 8

we have to check for multiplication:
so, \(1 \cdot (-1)=(-1) \cdot 1=-1\) and \(-1\) belongs to your set
\(1 \cdot 1=1\) and \(1\) belongs to your set
\((-1) \cdot (-1)=1\) and \(1\) belongs to your set
so, what can you conclude?

Answer 9

multiplication is right

Answer 10

correct!

Answer 11

ok, would division also work

Answer 12

yes! also division works!

Answer 13

yay, awesome thank you so much

Answer 14

:)

Answer 15

can you help me with a few more?

Answer 16

ok! Please open a new question

Answer 17

ok