Prove that the rational numbers are closed under addition. Complete the explanation.
O and s 0.Then
and
Let P.4,r, and s be integers with a
definition.
are rational numbers by
9
5
115 + 7
+
9
5
915
We know that ps, gr, and as are integers because the product of integer factors is
(select)
Ps-r is also an integer because integers are closed under
addition, and as (select) Co because q + 0 and s + 0.
number and therefore, the sum of two rational
Ps+gr
Thus,
is (select)
9 s
numbers is a rational number.