Answer:
(a) Set of rational numbers
(b) [tex]\pi + (-\pi) = 0[/tex]
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
[tex]a -b = c[/tex]
Where
a, b, c are of the same set.
The above is only true for rational numbers.
e.g.
[tex]1 - 2 = -1[/tex]
[tex]5 - 5 = 0[/tex]
[tex]\frac{1}{2} - \frac{1}{4} = \frac{1}{2}[/tex]
[tex]4 - 2 = 2[/tex]
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
[tex]a -b = c[/tex]
Where
a, b, c are of the same set.
In the given options (a) to (d), only
[tex]\pi + (-\pi) = 0[/tex] is not close under addition because:
[tex]\pi[/tex] is irrational while [tex]0[/tex] is rational
In other words, they belong to different set
