명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.4절

Sundstrom, Mathematical Reasoning · 2.4절영어 원문

Use counterexamples to explain why each of the following statements is false.

For each real number $x$ , if $x$ is positive, then $2x^2 > x$ .

정답·풀이 보기 (영어 원문)

A counterexample is $x = \dfrac{1}{4}$ since $\dfrac{1}{4}$ is positive and $2 \left( \dfrac{1}{4} \right)^2 = \dfrac{1}{8}$ and $\dfrac{1}{8} \leq \dfrac{1}{4}$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.4절영어 원문

Use counterexamples to explain why each of the following statements is false.

For each integer $n$ , $\left( n^2 + n + 1 \right)$ is a prime number.

다 풀었으면 정답 확인

A counterexample is $n = 4$ since $4^2 + 4 + 1 = 21$ , and 21 is not prime.

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