Please help on test
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Answer:
The closure property of the integers means that if we have a and b, integers then:
a + b = c will also be an integer.
(i will also use the fact that if a and b are integers, then a*b is also an integer)
Now suppose that we have two rational numbers.
a/b and c/d.
where a, b, c and d are integers. (b and d are different than zero)
the sum of those two numbers can be written as:
Now, a*d, b*c and b*d are integers (because integers are closed under multiplication)
and because a*d and b*c are integers, then:
a*d + b*c is also an integer.
Then:
(a*d + b*c)/(b*d)
is the quotient between two integers, which is a rational number.
Then we can conclude that the rational numbers are closed under the addition operation.