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:
[tex]-1+1=0 \\ -1+(-1)=-2 \\ 1+1=2[/tex]
-2, 0, 2 aren't in the set, so the set isn't closed under addition.
Subtraction:
[tex]-1-1=-2 \\
1-(-1)=2 \\ -1-(-1)=0 \\ 1-1=0[/tex]
-2, 0, 2 aren't in the set, so the set isn't closed under subtraction.
Multiplication:
[tex]-1 \times 1=-1 \\ -1 \times (-1)=1 \\ 1 \times 1=1[/tex]
-1 and 1 are in the set, so the set is closed under multiplication.
Division:
[tex]\frac{-1}{1}=-1 \\
\frac{1}{-1}=-1 \\ \frac{-1}{-1}=1 \\ \frac{1}{1}=1[/tex]
-1 and 1 are in the set, so the set is closed under division.
The answers are C and D.
