명제의 증명과 절대부등식 연습문제 — Sundstrom, Mathematical Reasoning · 3.1절 · 4a번

Sundstrom, Mathematical Reasoning · 3.1절 · 4a번영어 원문

Complete the following.

If $x$ and $y$ are integers and $xy=1$ , explain why $x=1$ or $x=-1$ .

정답·풀이 보기 (영어 원문)

If $xy = 1$ , then $x$ and $y$ are both divisors of $1$ , and the only divisors of $1$ are $-1$ and $1$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 3.1절 · 2d번영어 원문

For each of the following, use a counterexample to prove the statement is false.

For each integer $a$ , if 4 divides $\left( a^2 - 1 \right)$ , then 4 divides $(a - 1)$ .

다 풀었으면 정답 확인

The integer $a = 3$ is a counterexample since $a^2 - 1 = 8$ and $a - 1 = 2$ . Since 4 divides 8 and 4 does not divide 2, this is an example where the hypothesis of the conditional statement is true and the conclusion is false.

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