Discrete Math **Prove or disprove that if $ a, b \in \mathbb{Q} $ are rational numbers, then $ ab $ is also rational.**---In this statement, we are asked to determine whether the product of two rational numbers is always rational. Explanation:- Let $ a $ and $ b $ be rational numbers. By definition, rational numbers can be expressed in the form $ \frac{m}{n} $ where $ m $ and $ n $ are integers, and $ n \neq 0 $.- Suppose $ a = \frac{p}{q} $ and $ b = \frac{r}{s} $, where $ p, q, r, s $ are integers and $ q, s \neq 0 $.- Then, the product $ ab = \frac{p}{q} \times \frac{r}{s} = \frac{pr}{qs} $.- Since the product of integers $ pr $ and $ qs $ is also an integer and $ qs \neq 0 $, $ ab $ is in the form $ \frac{x}{y} $ where $ x $ and $ y $ are integers, and $ y \neq 0 $.- Hence, $ ab $ is a rational number.Thus, the statement is true: the product of two rational numbers is always a rational number.

Statement: If a and b are rational number then ab is also rational.

Answered: Prove or disprove that if a, b E Q are…

Math

Advanced Math

Prove or disprove that if a, b E Q are rational numbers, then ab is also rational.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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