명제와 조건 연습문제 — Sundstrom, Mathematical Reasoning · 1.1절

Sundstrom, Mathematical Reasoning · 1.1절영어 원문

Use the techniques of exploration to investigate each of the following statements. Can you make a conjecture as to whether the statement is true or false? Can you determine whether it is true or false?

There are integers $x$ and $y$ such that $2x+5y=41$ .

정답·풀이 보기 (영어 원문)

This proposition is true, as we can see by using $x = 3$ and $y = 7$ . We could also use $x = -2$ and $y = 9$ . There are many other possible choices for $x$ and $y$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 2.1절 · 4c번영어 원문

Suppose that $P$ and $Q$ are statements for which $Q$ is false and $\neg P \to Q$ is true (and it is not known if $R$ is true or false). What conclusion (if any) can be made about the truth value of each of the following statements?

$P \wedge R$

다 풀었으면 정답 확인

Statement $P$ is true but since we do not know if $R$ is true or false, we cannot tell if $P \wedge R$ is true or false.

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