Which set is closed under subtractionWhich answer choice shows that the set of irrational numbers is not closed under addition

(a) Set of rational numbers

(b)

Step-by-step explanation:

Solving (a): Set that is closed under subtraction

The solution to this is rational numbers.

For a set of number to be closed under subtraction, the following condition must be true

Where

a, b, c are of the same set.

The above is only true for rational numbers.

e.g.

The operations and the result in the above samples are rational numbers.

Solving (b): Choice not close under addition[See attachment for options]

As stated in (a)

For a set of number to be closed under subtraction, the following condition must be true

Where

a, b, c are of the same set.

In the given options (a) to (d), only

is not close under addition because:

is irrational while is rational

In other words, they belong to different set

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b