Question

Does subtraction exhibit a property of closure over the set of real numbers? Is subtraction commutative? If not, give an example to demonstrate.

Answer 1

Subtraction exhibit a property of closure over the set of real numbers because if you subtract two numbers from the real numbers set, the result will still be  a real number.

Example:
Let RS be a set of real numbers.
RS = {1, 2, 3}
Suppose I get 3 and subtract 1, 3 - 1, the result is 2 which is a real number. We can try a non-commutative 1 - 3 and yet it will still give us a real number which is -2.

Subtraction is non-commutative because if we interchange numbers in subtraction, the result will either be positive or negative.

Example:
3 - 1 = 2. The answer is 2; but we can not say this is true for 1 - 3 because it will yield -2.