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?

$\left(a+b \right)^2=a^2+b^2$ , for all real numbers $a$ and $b$ .

정답·풀이 보기 (영어 원문)

This proposition is false. A counterexample is $a = 2$ and $b = 1$ . For these values, $\left( {a + b} \right)^2 = 9$ and $a^2 + b^2 = 5$ .

한 번 더 — 비슷한 문제Sundstrom, 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?

If $x$ is an even integer, then $x^2$ is an even integer.

다 풀었으면 정답 확인

This proposition appears to be true. Anytime we use an example where $x$ is an even integer, the number $x^2$ is an even integer. However, we cannot claim that this is true based on examples since we cannot list all of the examples where $x$ is an even integer.

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