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.

$\left( \forall x \in \mathbb{R} \right) \left[ \sin ( {2x} ) = 2 ( {\sin x} ) ( {\cos x} ) \right]$ .

정답·풀이 보기 (영어 원문)

For each real number $x$ , $\sin ( {2x} ) = 2( {\sin x} )( {\cos x} )$ . - $(\exists x \in \mathbb{R})( \sin ( {2x} ) \ne 2( {\sin x} )( {\cos x} ))$ . - There exists a real number $x$ such that $\sin \left( {2x} \right) \ne 2\left( {\sin x} \right)\left( {\cos x} \right)$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.4절 · 4e번영어 원문

Write each of the following statements as an English sentence that does not use the symbols for quantifiers.

$\left( {\exists n} \in \mathbb{Z} \right)\left( {\forall m} \in \mathbb{Z} \right)\left( {m^2 > n} \right)$

다 풀었으면 정답 확인

There exists an integer $n$ such that for each integer $m$ , $m^2 > n$ .

이 문제로 이어서 풀기

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