Question

Tell whether the set is closed under the operation. If it is not closed, justify your answer using an example. A. Set of negative rational numbers; multiplication. B. {0, 1}; multiplication.

Answer 1

Part A
Set of rational negative numbers is not closed under multiplication

Part B
The set {0,1} is closed under multiplication

Explanation:

A set is closed under some operation if applying the operation on any elements of the set gives an element which is still in that set.

Part A
Set of rational negative numbers is not closed under multiplication

If we take two rational negative numbers and apply multiplication operation we will end up with a positive number which is not in the original set.

For example, -2 and -1 are two rational negative numbers

But -2 x -1 = +2 which is not in the set of rational negative numbers

Part B

The set {0,1} is closed under multiplication because
0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1

all of which are in the original set.

Hope that helps