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

Sundstrom, 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 $6 \mid b$ .

정답·풀이 보기 (영어 원문)

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.

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 3.2절 · 3a번영어 원문

Complete the following.

Write the contrapositive of the following statement: For all positive real numbers $a$ and $b$ , if $\sqrt {ab} \ne \dfrac{{a + b}}{2}$ , then $a \ne b$ .

다 풀었으면 정답 확인

The contrapositive is: For all positive real numbers $a$ and $b$ , if $a = b$ , then $\sqrt{ab} = \dfrac{a + b}{2}$ .

이 문제로 이어서 풀기

# 명제의 증명과 절대부등식개념 확인자동 분류