Final answer:
The statement is true: the product of two rational numbers is indeed a rational number, since the product of integers is an integer and the definition of a rational number is such a quotient with a non-zero denominator.
Step-by-step explanation:
The statement that if a and b are rational numbers, then ab is also rational is true. Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. If we have two rational numbers, let’s say − where ≈, β≈ℤ, and − ≈ β ≠ 0, and − where δ≈, ε≈ℤ, and − ≈ ε ≠ 0 — their product would be (−)×(−) = αδ − βε. Since both αδ and βε are also integers (integers are closed under multiplication), and βε ≠ 0 (as neither β nor ε are zero), the product is also a ratio of two integers with a non-zero denominator, thus a rational number.