명제와 조건 연습문제 (공통수학2)

101.Sundstrom, Mathematical Reasoning · 2.1절 · 8a번영어 원문

Suppose each of the following statements is true.

Laura is in the seventh grade. - Laura got an A on the mathematics test or Sarah got an A on the mathematics test. - If Sarah got an A on the mathematics test, then Laura is not in the seventh grade.

If possible, determine the truth value of each of the following statements. Carefully explain your reasoning.

Laura got an A on the mathematics test.

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

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

# 명제와 조건계산자동 분류

102.Sundstrom, Mathematical Reasoning · 2.1절 · 8b번영어 원문

Suppose each of the following statements is true.

Laura is in the seventh grade. - Laura got an A on the mathematics test or Sarah got an A on the mathematics test. - If Sarah got an A on the mathematics test, then Laura is not in the seventh grade.

If possible, determine the truth value of each of the following statements. Carefully explain your reasoning.

Sarah got an A on the mathematics test.

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

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

# 명제와 조건계산자동 분류

103.Sundstrom, Mathematical Reasoning · 2.1절 · 8c번영어 원문

Suppose each of the following statements is true.

Laura is in the seventh grade. - Laura got an A on the mathematics test or Sarah got an A on the mathematics test. - If Sarah got an A on the mathematics test, then Laura is not in the seventh grade.

If possible, determine the truth value of each of the following statements. Carefully explain your reasoning.

Either Laura or Sarah did not get an A on the mathematics test.

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 1번

# 명제와 조건계산자동 분류

104.Sundstrom, Mathematical Reasoning · 2.1절 · 9a번영어 원문

Let $P$ stand for “the integer $x$ is even,” and let $Q$ stand for “ $x^2$ is even.” Express the conditional statement $P \to Q$ in English using

The “if then” form of the conditional statement

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 5a번

# 명제와 조건계산자동 분류

105.Sundstrom, Mathematical Reasoning · 2.1절 · 9b번영어 원문

Let $P$ stand for “the integer $x$ is even,” and let $Q$ stand for “ $x^2$ is even.” Express the conditional statement $P \to Q$ in English using

The word “implies”

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 5b번

# 명제와 조건계산자동 분류

106.Sundstrom, Mathematical Reasoning · 2.1절 · 9c번영어 원문

Let $P$ stand for “the integer $x$ is even,” and let $Q$ stand for “ $x^2$ is even.” Express the conditional statement $P \to Q$ in English using

The “only if” form of the conditional statement

정답·풀이 보기 (영어 원문)

The integer $x$ is even only if $x^2$ is even.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 2c번

# 명제와 조건계산자동 분류

107.Sundstrom, Mathematical Reasoning · 2.1절 · 11a번영어 원문

For statements $P$ and $Q$ , use truth tables to determine if each of the following statements is a tautology, a contradiction, or neither.

$\neg Q \vee (P \to Q)$ .

정답·풀이 보기 (영어 원문)

$\neg Q \vee (P \to Q)$ is a tautology.

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

# 명제와 조건계산자동 분류

108.Sundstrom, Mathematical Reasoning · 2.1절 · 11b번영어 원문

For statements $P$ and $Q$ , use truth tables to determine if each of the following statements is a tautology, a contradiction, or neither.

$Q \wedge (P \wedge \neg Q)$ .

정답·풀이 보기 (영어 원문)

$Q \wedge (P \wedge \neg Q)$ is a contradiction.

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

# 명제와 조건계산자동 분류

109.Sundstrom, Mathematical Reasoning · 2.1절 · 11c번영어 원문

For statements $P$ and $Q$ , use truth tables to determine if each of the following statements is a tautology, a contradiction, or neither.

$(Q \wedge P) \wedge (P \to \neg Q)$ .

정답·풀이 보기 (영어 원문)

$(Q \wedge P) \wedge (P \to \neg Q)$ is a contradiction.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 1.1절 · 2a번

# 명제와 조건계산자동 분류

110.Sundstrom, Mathematical Reasoning · 2.1절 · 11d번영어 원문

For statements $P$ and $Q$ , use truth tables to determine if each of the following statements is a tautology, a contradiction, or neither.

$\neg Q \to (P \wedge \neg P)$ .

정답·풀이 보기 (영어 원문)

$\neg Q \to (P \wedge \neg P)$ is neither a tautology nor a contradiction.

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

# 명제와 조건계산자동 분류

111.Sundstrom, Mathematical Reasoning · 2.1절 · 12a번영어 원문

For statements $P$ , $Q$ , and $R$ :

Show that $\left[ (P \to Q) \wedge P \right] \to Q$ is a tautology.

Note: In symbolic logic, this is an important logical argument form called modus ponens.

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

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

# 명제와 조건증명·논술자동 분류

112.Sundstrom, Mathematical Reasoning · 2.1절 · 12b번영어 원문

For statements $P$ , $Q$ , and $R$ :

Show that $\left[ (P \to Q) \wedge (Q \to R) \right] \to (P \to R)$ is a tautology.

Note: In symbolic logic, this is an important logical argument form called syllogism.

원본 교재에 이 문제의 정답은 실려 있지 않습니다.

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

# 명제와 조건증명·논술자동 분류

113.Sundstrom, Mathematical Reasoning · 2.2절 · 1a번영어 원문

Write the converse and contrapositive of each of the following conditional statements.

If $a = 5$ , then $a^2 = 25$ .

정답·풀이 보기 (영어 원문)

Converse: If $a^2 = 25$ , then $a = 5$ . Contrapositive: If $a^2 \ne 25$ , then $a \ne 5$ .

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

# 명제와 조건계산자동 분류

114.Sundstrom, Mathematical Reasoning · 2.2절 · 1b번영어 원문

Write the converse and contrapositive of each of the following conditional statements.

If it is not raining, then Laura is playing golf.

정답·풀이 보기 (영어 원문)

Converse: If Laura is playing golf, then it is not raining. Contrapositive: If Laura is not playing golf, then it is raining.

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

# 명제와 조건계산자동 분류

115.Sundstrom, Mathematical Reasoning · 2.2절 · 1c번영어 원문

Write the converse and contrapositive of each of the following conditional statements.

If $a \ne b$ , then $a^4 \ne b^4$ .

정답·풀이 보기 (영어 원문)

Converse: If $a^4 \ne b^4$ , then $a \ne b$ . Contrapositive: If $a^4 = b^4$ , then $a = b$ .

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

# 명제와 조건계산자동 분류

116.Sundstrom, Mathematical Reasoning · 2.2절 · 1d번영어 원문

Write the converse and contrapositive of each of the following conditional statements.

If $a$ is an odd integer, then $3a$ is an odd integer.

정답·풀이 보기 (영어 원문)

Converse: If $3a$ is an odd integer, then $a$ is an odd integer. Contrapositive: If $3a$ is an even integer, then $a$ is an even integer.

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

# 명제와 조건계산자동 분류

117.Sundstrom, Mathematical Reasoning · 2.2절 · 3a번영어 원문

Write a useful negation of each of the following statements. Do not leave a negation as a prefix of a statement. For example, we would write the negation of “I will play golf and I will mow the lawn” as “I will not play golf or I will not mow the lawn.”

We will win the first game and we will win the second game.

정답·풀이 보기 (영어 원문)

We will not win the first game or we will not win the second game.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 11a번

# 명제와 조건활용자동 분류

118.Sundstrom, Mathematical Reasoning · 2.2절 · 3b번영어 원문

Write a useful negation of each of the following statements. Do not leave a negation as a prefix of a statement. For example, we would write the negation of “I will play golf and I will mow the lawn” as “I will not play golf or I will not mow the lawn.”

They will lose the first game or they will lose the second game.

정답·풀이 보기 (영어 원문)

They will not lose the first game and they will not lose the second game.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 11d번

# 명제와 조건활용자동 분류

119.Sundstrom, Mathematical Reasoning · 2.2절 · 3c번영어 원문

Write a useful negation of each of the following statements. Do not leave a negation as a prefix of a statement. For example, we would write the negation of “I will play golf and I will mow the lawn” as “I will not play golf or I will not mow the lawn.”

If you mow the lawn, then I will pay you $20.

정답·풀이 보기 (영어 원문)

You mow the lawn and I will not pay you $20.

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

# 명제와 조건계산자동 분류

120.Sundstrom, Mathematical Reasoning · 2.2절 · 3d번영어 원문

Write a useful negation of each of the following statements. Do not leave a negation as a prefix of a statement. For example, we would write the negation of “I will play golf and I will mow the lawn” as “I will not play golf or I will not mow the lawn.”

If we do not win the first game, then we will not play a second game.

정답·풀이 보기 (영어 원문)

We do not win the first game and we will play a second game.

한 번 더 — 비슷한 문제 풀기Sundstrom, Mathematical Reasoning · 2.1절 · 11b번

# 명제와 조건활용자동 분류