명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 1.1절

Sundstrom, Mathematical Reasoning · 1.1절영어 원문

Answer each of the following questions.

Is the set of rational numbers closed under subtraction? Explain.

정답·풀이 보기 (영어 원문)

The set of rational numbers is closed under subtraction since $\dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad-bc}{bd}$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 1.1절영어 원문

Use the techniques of exploration to investigate each of the following statements. Can you make a conjecture as to whether the statement is true or false? Can you determine whether it is true or false?

If $x$ and $y$ are odd integers, then $x \cdot y$ is an odd integer.

다 풀었으면 정답 확인

This proposition appears to be true. Anytime we use an example where $x$ and $y$ are both odd integers, the number $x \cdot y$ is an odd integer. However, we cannot claim that this is true based on examples since we cannot list all of the examples where both $x$ and $y$ are odd integers.

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