명제의 증명과 절대부등식 연습문제 — Sundstrom, Mathematical Reasoning · 3.3절 · 1a번

Sundstrom, Mathematical Reasoning · 3.3절 · 1a번영어 원문

This exercise is intended to provide another rationale as to why a proof by contradiction works. Suppose that we are trying to prove that a statement $P$ is true. Instead of proving this statement, assume that we prove that the conditional statement “If $\neg P$ , then $C$ ” is true, where $C$ is some contradiction. Recall that a contradiction is a statement that is always false.

In symbols, write a statement that is a disjunction and that is logically equivalent to $\neg P \to C$ .

정답·풀이 보기 (영어 원문)

$P \vee C$

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 3.3절 · 11a번영어 원문

Justify your conclusion for each of the following.

Is the base 2 logarithm of 32, $\log_2 (32)$ , a rational number or an irrational number?

다 풀었으면 정답 확인

Recall that $\log _2 (32)$ is the real number $a$ such that $2^a = 32$ . That is, $a = \log _2 (32)$ means that $2^a = 32$ . If we assume that $a$ is rational, then there exist integers $m$ and $n$ , with $n \ne 0$ , such that $a = \dfrac{m}{n}$ .

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