명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.4절

Sundstrom, Mathematical Reasoning · 2.4절영어 원문

For each of the following statements

(1) Write the statement in the form of an English sentence that does not use the symbols for quantifiers. - (2) Write the negation of the statement in a symbolic form that does not use the negation symbol. - (3) Write the negation of the statement in the form of an English sentence that does not use the symbols for quantifiers.

$\left( \exists x \in \mathbb{R} \right) \left( x^2 + 1 = 0 \right)$ .

정답·풀이 보기 (영어 원문)

There exists a real number $x$ such that $x^2 + 1 = 0$ . - $(\forall x \in \mathbb{R}) \left( \text{ } x^2 + 1 \ne 0 \right)$ . - For each real number $x$ , $x^2 + 1 \ne 0$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.4절 · 2b번영어 원문

For each of the following, use a counterexample to show that the statement is false. Then write the negation of the statement in English, without using symbols for quantifiers.

$\left( {\forall x \in \mathbb{R}} \right)\left( {x^2 > 0} \right)$ .

다 풀었으면 정답 확인

$x = 0$ is a counterexample. The negation is: There exists a real number $x$ such that $x^2 \leq 0$ .

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