Answer: Integers are closed under multiplication.
Step-by-step explanation:
Rational numbers are numbers of the form:
a/b
such that a and b are integers.
The axiom: " Integers are closed under multiplication. "
Says that if we have two integers, x and y, then:
x*y is also an integer.
So if we have two rational numbers,
a/b and c/d
Such that a, b, c and d are integers, and we multiply them, we have:
(a/b)*(c/d) = (a*c/b*d)
the numerator is a*c is the product of two integers, so this is an integer by the previous axiom.
the denominator is b*d, also a product of integers, so this is an integer.
then (a*d)/(b*d) is the quotient of two integers, then this is a rational number.