Logic Validity: Modus Ponens and More

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Questions and Answers

Which of the following represents a valid argument form in formal reasoning?

If A then B; Not B; So, Not A

If A then B; B; So, A

If A then B; A; So, B (correct)

If A then B; Not A; So, Not B

What type of fallacy is represented by denying the antecedent?

Denying the Antecedent (correct)

Modus Tollens

Modus Ponens

Affirming the Consequent

In the example "If Tom lives in Kingston, then he lives in Jamaica," what can be inferred if it is not true that Tom lives in Jamaica?

Tom lives in Kingston.

Tom cannot be in Jamaica.

Tom lives somewhere else.

Tom does not live in Kingston. (correct)

Which of the following is a characteristic of a valid argument in hypothetical syllogism?

If A then B; If B then C; So, If A then C Signup and view all the answers

What is produced by the combination of valid argument forms Modus Ponens and Modus Tollens?

Sound reasoning Signup and view all the answers

In formal reasoning, how does a counter-example function?

It disproves the argument's claim. Signup and view all the answers

Which conclusion can be drawn from the statement "If John is lying, then you are innocent and John’s mother is guilty" if it is given that John is lying?

You are innocent and John’s mother is guilty. Signup and view all the answers

What is the primary flaw in denying the antecedent?

It relies on the truth of the consequent only. Signup and view all the answers

What characterizes a valid argument?

It has true premises that guarantee the conclusion. Signup and view all the answers

Which of the following describes an example of affirming the consequent?

If it rains, the ground is wet. The ground is wet. Therefore, it rained. Signup and view all the answers

What is the conclusion of the argument: If Tom loves his dog, then Tom wants his dog to be happy; If Tom wants his dog to be happy, then Tom will walk his dog every day?

Tom will walk his dog every day. Signup and view all the answers

Which of the following exemplifies a formal fallacy?

If Tom is in Kingston, then he is not at home; Tom is not in Kingston; therefore, he is at home. Signup and view all the answers

What distinguishes a disjunctive syllogism from other argument forms?

It requires two premises, one of which is a disjunction. Signup and view all the answers

In a disjunctive syllogism, which statement correctly represents its structure?

Either A or B; Not A; therefore, B. Signup and view all the answers

In formal reasoning, what is a conditional statement?

It indicates a relationship between two propositions. Signup and view all the answers

Which of the following arguments is invalid due to the fallacy of denying the antecedent?

If it's a dog, then it barks. It is not a dog, so it does not bark. Signup and view all the answers

What is the main characteristic of a hypothetical syllogism?

It consists of two premises leading to a logical conclusion. Signup and view all the answers

Which scenario represents a false conclusion arising from true premises?

If all dogs are animals, and all cats are animals, therefore all dogs are cats. Signup and view all the answers

Which statement best exemplifies a valid argument using a disjunctive syllogism?

Either the car is in the garage or on the street; the car is on the street; therefore, it is not in the garage. Signup and view all the answers

Which best defines a common mistake found in formal reasoning?

Ignoring existing premises when forming a conclusion. Signup and view all the answers

What indicates a premise is guaranteed to lead to an invalid conclusion?

At least one false premise. Signup and view all the answers

Which of the following statements illustrates the concept of a conditional statement?

If it is sunny, then we will go for a picnic. Signup and view all the answers

Which of the following best exemplifies a valid argument structure?

If E, then F. E is true, thus F is true. Signup and view all the answers

What is the result of stating: If A or B is true, and A is not true, what can we conclude?

B is true. Signup and view all the answers

Study Notes

Valid Arguments

Modus Ponens (MP) is a valid argument form with two premises and a conclusion. The premises are a conditional statement (If A then B) and the affirmation of the antecedent (A). The conclusion is the consequent (B).
Modus Tollens (MT) is also a valid argument form with two premises and a conclusion. The premises are a conditional statement (If A then B) and the negation of the consequent (Not B). The conclusion is the negation of the antecedent (Not A).
Hypothetical Syllogism (HS) is a valid argument form with two conditional statements (If A then B and If B then C) and a conclusion (If A then C).
Disjunctive Syllogism (DS) is a valid argument form with two premises and a conclusion, where the first premise is a disjunctive statement (Either A or B) and the second premise is the negation of one of the disjuncts (Not A or Not B). The conclusion is the remaining disjunct (B or A).

Invalid Arguments

Affirming the Consequent (AC) is an invalid argument form, also a formal fallacy. It has a conditional statement (If A then B) and the affirmation of the consequent (B). The conclusion is the antecedent (A).
Denying the Antecedent (DA) is also an invalid argument form, a formal fallacy. The premises are a conditional statement (If A then B) and the negation of the antecedent (Not A). The conclusion is the negation of the consequent (Not B).
Unsound arguments are a type of invalid argument, where at least one of the premises is false.

Other Key Facts

Conditional Statements are also known as “hypothetical statements”
A syllogism is a three-step argument with two premises and one conclusion.
“A or B” is called the disjunction of statements “A” and “B”.
Arguments with the valid forms MP, MT, HS, and DS are valid.

Studying That Suits You

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Description

Test your understanding of valid arguments like Modus Ponens, Modus Tollens, Hypothetical Syllogism, and Disjunctive Syllogism. This quiz will challenge your skills in identifying and applying these logical structures. Perfect for students of formal logic and reasoning.