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

A set is closed under an operation if performing the operation on the numbers in the set results in a number that is in the set.

Addition:
$-1+1=0 \\ -1+(-1)=-2 \\ 1+1=2$
-2, 0, 2 aren't in the set, so the set isn't closed under addition.

Subtraction:
$-1-1=-2 \\ 1-(-1)=2 \\ -1-(-1)=0 \\ 1-1=0$
-2, 0, 2 aren't in the set, so the set isn't closed under subtraction.

Multiplication:
$-1 \times 1=-1 \\ -1 \times (-1)=1 \\ 1 \times 1=1$
-1 and 1 are in the set, so the set is closed under multiplication.

Division:
$\frac{-1}{1}=-1 \\ \frac{1}{-1}=-1 \\ \frac{-1}{-1}=1 \\ \frac{1}{1}=1$
-1 and 1 are in the set, so the set is closed under division.

The answers are C and D.