Lesson 41 : Tautologies and Fallacies

Slide 1

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Tautologies and Fallacies

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3. Solve the LAS

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Tautologies and Fallacies

1 / 10

Which of the following is an example of a fallacy denying the hypothesis?

a. If I will not take a bath, then I cannot go to school.

b. If I will love you, then you will love me too.

c. Assuming that I will study my lesson, then I will not pass the test.

d. Assuming that I will not go to school every day, then I will not fail.

2 / 10

Carmela loves both Badminton and Volleyball, but she loves neither Badminton nor Tennis. The given statement is a:

a. tautology

b. fallacy

c. both tautology and fallacy

d. neither tautology not fallacy

3 / 10

Carmela loves both Badminton and Volleyball, but she loves neither Badminton nor Tennis. Express the statement to a mathematical symbol.

a. (𝑝∧𝑞)∧(𝑞∧𝑟)

b. (𝑝∧𝑞)∧(∼𝑞∧∼𝑟)

c. (𝑝∧∼𝑝)∧(∼𝑞∧𝑟)

d. (∼𝑝∧∼𝑞)∧(𝑞∧𝑟)

4 / 10

Which of the following statement is a fallacy?

a. The dog is either brown, or the dog is not brown.

b. Today is a rainy day or a sunny day.

c. If tomorrow is Monday, then today is Saturday.

d. Today is a hot day if and only if it is a sunny day.

5 / 10

Which of the following statements is represented by the logical symbol of the
tautology 𝑝 ∧ ∼(p∨q)?

a. Jeff likes Music but he does not like Music and Arts

b. Jeff likes Music but he does not like Music or Arts

c. Jeff likes Music nor he does not like Music or Arts.

d. Jeff likes Music but he does not like either Music or Arts

6 / 10

Which of the following is a tautology?

a. Michael is an artist or not an artist.

b. Michael is an artist and a singer.

c. It is not true that Michael is both an artist and a singer

d. Michel is not a singer.

7 / 10

Which of the following is a tautology?

a. [(𝑝→𝑞)∧𝑝]→𝑝

b. (𝑝→𝑞)↔(~𝑞→𝑝)

c. [[𝑝→(𝑟→𝑞)]↔[(𝑝∧𝑟)→𝑞]

d. (𝑝→𝑟)∧[(𝒑↔𝒓)→𝑞]→(𝑝→𝑞)

8 / 10

Which of the following is NOT a tautology?

a. Maria is smart, or she is not smart.

b. Either you will pass the interview, or you will fail in the interview.

c. Anna loves Arts or she does not love Arts.

d. Today is a not lucky day and tomorrow is a lucky day.

9 / 10

Which of the following is a fallacy?

a. It is a compound statement that is always true.

b. It is a compound statement that is not always true.

c. It is a compound statement that is sometimes true.

d. It is a compound statement that is neither true nor false.

10 / 10

Which of the following is a tautology?

a. It is a compound statement that is always true.

b. It is a compound statement that is not always true.

c. It is a compound statement that is sometimes true.

d. It is a compound statement that is neither true nor false.

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