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

정답·풀이 보기 (영어 원문)

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

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.3절영어 원문

Let $P( x )$ be the predicate “ $x^2 \leq 9$ .”

If the universal set is $\mathbb{R}$ , describe the truth set of $P(x)$ using English and write the truth set of $P( x )$ using set builder notation.

다 풀었으면 정답 확인

The truth set is the set of all real numbers whose square is less than or equal to 9. The truth set is $\left\{ {\left. {x \in \mathbb{R} } \right| x^2 \leq 9} \right\} = \left\{ \left. x \in \mathbb{R} \right| -3 \leq x \leq 3 \right\}$ .

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