Question

The set {-1, 0, 1} is closed under how many of these operations:
addition, subtraction, multiplication, division, square root

A) 1
B) 2
C) 3
D) 4
E) 5

Answer 1

when you apply an operation on any two numbers in the set (same number is allowed) and get an answer that is not in the set, then the set in not closed in that operation

Answer 2

(-1) PLUS (-1) = (-2), a number not belonging to the set. therefore the set is not closed under addition

Answer 3

Oh this makes sense now. So it only closed under multiplication?

Answer 4

right it is.

Answer 5

I see. Thanks!

Answer 6

Try using all combinations of 2 of those numbers:
-1 ___ 0
-1 ___ 1
0 ___ 1
Now substitute ___ with +, then -, then *, then /.
Fianlly take the square root of each number.
If while doing any of the above operations, you get a numbe that is not in the set, that set is not closed for that operation.