명제의 증명과 절대부등식 연습문제 — Sundstrom, Mathematical Reasoning · 3.1절 · 3g번

Sundstrom, Mathematical Reasoning · 3.1절 · 3g번영어 원문

Determine if each of the following statements is true or false. If a statement is true, then write a formal proof of that statement, and if it is false, then provide a counterexample that shows it is false.

For all integers $a$ , $b$ , and $d$ with $d \ne 0$ , if $d$ divides both $a-b$ and $a+b$ , then $d$ divides $a$ .

정답·풀이 보기 (영어 원문)

This statement is false. One counterexample is $a = 7$ , $b = 1$ , and $d = 2$ . Why is this a counterexample?

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 3.1절 · 3b번영어 원문

Determine if each of the following statements is true or false. If a statement is true, then write a formal proof of that statement, and if it is false, then provide a counterexample that shows it is false.

For all integers $a$ and $b$ with $a \ne 0$ , if $6 \mid \left(ab \right)$ , then $6 \mid a$ or $6 \mid b$ .

다 풀었으면 정답 확인

This statement is false. One counterexample is $a = 3$ and $b = 2$ since this is an example where the hypothesis is true and the conclusion is false.

이 문제로 이어서 풀기

# 명제의 증명과 절대부등식개념 확인자동 분류