명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 2.3절

Sundstrom, Mathematical Reasoning · 2.3절영어 원문

Assume the universal set for all variables is $\mathbb{Z}$ , and let $R( {x,\;y,\;z} )$ be the predicate “ $x^2 + y^2 = z^2$ .”

(i) Find two different examples for which $R( {x, y, z})$ is false.

(ii) Find two different examples for which $R( {x, y, z})$ is true.

정답·풀이 보기 (영어 원문)

(i) Two examples for which $R( {x, y, z} )$ is false are: $x = 1$ , $y = 1$ , $z = 1$ and $x = 3$ , $y = - 1$ , $z = 5$ .

(ii) Two examples for which $R( {x, y, z} )$ is true are: $x = 3$ , $y = 4$ , $z = 5$ and $x = 5$ , $y = 12$ , $z = 13$ .

한 번 더 — 비슷한 문제Sundstrom, 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.

$\left( \exists x \in \mathbb{Q} \right) \left( x^2 - 3x - 7 = 0 \right)$ .

다 풀었으면 정답 확인

There exists a rational number $x$ such that $x^2 - 3x - 7 = 0$ . - $(\forall x \in \mathbb{Q}) \left( x^2 - 3x - 7 \ne 0 \right)$ . - For each rational number $x$ , $x^2 - 3x - 7 \ne 0$ .

이 문제로 이어서 풀기

# 명제와 조건계산자동 분류