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

Ill give a medal

Answer 2

@TuringTest

Answer 3

Closure (under an operation) means that if you take any two things in the set, you operate on them, the result will also be in the set.
So for example, if we start with the set of positive integers,
N = { 1,2,3,4,5,... } , and pick two arbitrary elements, add them, the result is also in the set.
Example : 2 ,3 2+3 = 5 , and 5 is in N.

What about subtraction? Is the set closed {1,2,3,4... } closed under subtraction?
Is 3 - 5 in the set?

Answer 4

i think the answer might be subtraction but im not sure if thats right or if there are any others..

Answer 5

it is not closed under subtraction. (-1) -1 = -2 , and -2 is not in the set

Answer 6

how about multiplication

Answer 7

that could be right

Answer 8

1*1 = 1 , 1 is in {-1,1}. ✔
1* (-1) = -1 , -1 is in {-1,1} . ✔
(-1)*(-1)= 1 , 1 is in {-1,1} . ✔

Answer 9

that covers all the cases.
now try division, go through the cases

Answer 10

its confusing

Answer 11

1 ÷ 1= 1 ✔

(-1) ÷ 1= - 1 ✔

(-1) ÷ (-1)= 1 ✔

Answer 12

the result of any division is itself either 1 or -1 , a member of the set from which it originated