명제와 조건 연습문제 (공통수학2)

1.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 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절

# 명제와 조건개념 확인자동 분류

2.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 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 4c번

# 명제와 조건개념 확인자동 분류

3.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?

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

정답·풀이 보기 (영어 원문)

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.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절

# 명제와 조건개념 확인자동 분류

4.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?

If $x$ and $y$ are odd integers, then $x \cdot y$ is an odd integer.

정답·풀이 보기 (영어 원문)

This proposition appears to be true. Anytime we use an example where $x$ and $y$ are both odd integers, the number $x \cdot y$ is an odd integer. However, we cannot claim that this is true based on examples since we cannot list all of the examples where both $x$ and $y$ are odd integers.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절

# 명제와 조건개념 확인자동 분류

5.Sundstrom, Mathematical Reasoning · 1.1절 · 3a번영어 원문

Determine whether each of the following conditional statements is true or false.

If $10 \lt 7$ , then $3 = 4$ .

정답·풀이 보기 (영어 원문)

This statement is true.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.4절

# 명제와 조건개념 확인자동 분류

6.Sundstrom, Mathematical Reasoning · 1.1절 · 3b번영어 원문

Determine whether each of the following conditional statements is true or false.

If $7 \lt 10$ , then $3 = 4$ .

정답·풀이 보기 (영어 원문)

This statement is false.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절 · 1k번

# 명제와 조건개념 확인자동 분류

7.Sundstrom, Mathematical Reasoning · 1.1절 · 3c번영어 원문

Determine whether each of the following conditional statements is true or false.

If $10 \lt 7$ , then $3 + 5 = 8$ .

정답·풀이 보기 (영어 원문)

This statement is true.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절 · 6c번

# 명제와 조건개념 확인자동 분류

8.Sundstrom, Mathematical Reasoning · 1.1절 · 3d번영어 원문

Determine whether each of the following conditional statements is true or false.

If $7 \lt 10$ , then $3 + 5 =8$ .

정답·풀이 보기 (영어 원문)

This statement is true.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.2절 · 7b번

# 명제와 조건개념 확인자동 분류

9.Sundstrom, Mathematical Reasoning · 2.1절 · 1번영어 원문

Suppose that Daisy says, “If it does not rain, then I will play golf.” Later in the day you come to know that it did rain but Daisy still played golf. Was Daisy's statement true or false? Support your conclusion.

정답·풀이 보기 (영어 원문)

The statement was true. When the hypothesis is false, the conditional statement is true.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.4절

# 명제와 조건개념 확인자동 분류

10.Sundstrom, Mathematical Reasoning · 2.1절 · 4a번영어 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?

$\neg Q \to P$

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절

# 명제와 조건개념 확인자동 분류

11.Sundstrom, Mathematical Reasoning · 2.1절 · 4b번영어 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?

$P$

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절

# 명제와 조건개념 확인자동 분류

12.Sundstrom, 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?

$P \wedge R$

정답·풀이 보기 (영어 원문)

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.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절

# 명제와 조건개념 확인자동 분류

13.Sundstrom, Mathematical Reasoning · 2.1절 · 4d번영어 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?

$R \to \neg P$

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.2절 · 3d번

# 명제와 조건개념 확인자동 분류

14.Sundstrom, Mathematical Reasoning · 2.4절 · 6b번영어 원문

Assume that the universal set is $\mathbb{Z}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{Z}} \right)\left( {t \cdot x = 20} \right)$

.

.

If 5 is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

정답·풀이 보기 (영어 원문)

It is a true statement.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.4절 · 6a번

# 명제와 조건개념 확인자동 분류

15.Sundstrom, Mathematical Reasoning · 2.4절 · 6c번영어 원문

Assume that the universal set is $\mathbb{Z}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{Z}} \right)\left( {t \cdot x = 20} \right)$

.

.

If 8 is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

정답·풀이 보기 (영어 원문)

It is a false statement.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.4절 · 1c번

# 명제와 조건개념 확인자동 분류

16.Sundstrom, Mathematical Reasoning · 2.4절 · 6d번영어 원문

Assume that the universal set is $\mathbb{Z}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{Z}} \right)\left( {t \cdot x = 20} \right)$

.

.

If $-2$ is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

정답·풀이 보기 (영어 원문)

It is a true statement.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.4절

# 명제와 조건개념 확인자동 분류

17.Sundstrom, Mathematical Reasoning · 2.4절 · 7b번영어 원문

Assume that the universal set is $\mathbb{R}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{R}} \right)\left( {t \cdot x = 20} \right)$

.

If 5 is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절 · 1h번

# 명제와 조건개념 확인자동 분류

18.Sundstrom, Mathematical Reasoning · 2.4절 · 7c번영어 원문

Assume that the universal set is $\mathbb{R}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{R}} \right)\left( {t \cdot x = 20} \right)$

.

If $\pi$ is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.4절

# 명제와 조건개념 확인자동 분류

19.Sundstrom, Mathematical Reasoning · 2.4절 · 7d번영어 원문

Assume that the universal set is $\mathbb{R}$ . Consider the following sentence:

$\left( {\exists t \in \mathbb{R}} \right)\left( {t \cdot x = 20} \right)$

.

If $0$ is substituted for $x$ , is the resulting sentence a statement? If it is a statement, is the statement true or false?

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.2절 · 1d번

# 명제와 조건개념 확인자동 분류