Question

Positive numbers are not closed under subtraction. Give an example below.

Answer 1

A set S is said to be closed under subtraction if:

`\forall a,b\in S,\text{ a-b}\in S\text{ and b-a}\in S`

Since the set given is that of positive numbers, we pick two different positive numbers, say 6 and 9.

`\begin{gathered} \\ 9-6=3\in S \\ 6-9=-3\\otin S \end{gathered}`

Since -3 is not a positive number, we can then conclude that the set of positive numbers are