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# Study of Syllogisms and Negations

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@RestfulJuniper

### Which of the following statements correctly represents the modus ponens argument form?

If P, then Q. Q. Therefore, P.

### Which of the following represents the fallacy of affirming the consequent?

If P, then Q. Q. Therefore, P.

### Which of the following represents the modus tollens argument form?

If P, then Q. Not Q. Therefore, not P.

### Which of the following represents a false hypothetical syllogism?

<p>If P, then Q. If Q, then R. P. Therefore, R.</p> Signup and view all the answers

### Which of the following represents the fallacy of denying or negating the antecedent?

<p>If P, then Q. Not P. Therefore, not Q.</p> Signup and view all the answers

### Which of the following correctly represents the disjunctive syllogism argument form?

<p>P or Q. Not P. Therefore, Q.</p> Signup and view all the answers

### Which of the following statements accurately distinguishes between deduction and induction?

<p>All of the above.</p> Signup and view all the answers

### Which of the following statements accurately represents the difference between particular and general statements?

<p>Particular statements have a specific, countable, and finite reference class, while general statements have a non-specific, non-countable, and infinite reference class.</p> Signup and view all the answers

### Which of the following correctly represents a valid syllogistic argument form?

<p>All of the above.</p> Signup and view all the answers

### Which of the following statements accurately describes a syllogism?

<p>A syllogism is a form of deductive argument with two premises and one conclusion.</p> Signup and view all the answers

## Study Notes

### Valid Forms of Deductive Arguments

• All valid forms of deductive arguments are syllogisms.
• A note on interpreting negation: if the original statement is a negation, its negation will be positive, and vice versa.

### Types of Valid Deductive Forms

• Modus Ponens (affirming the antecedent): All mangoes are fruits; This thing is a mango; So it is a fruit.
• Modus Tollens (negating the consequent): All mangoes are fruits; This thing is not a fruit; So, this thing is not a mango.
• Hypothetical Syllogism: All mangoes are fruits; All fruits are edible; So, all mangoes are edible.
• Disjunctive Syllogism: You either save at Barclays or Stanchart; You do not save at Barclays; Therefore, you save at Stanchart.

### Formal/Syllogistic Fallacies

• The fallacy of affirming the consequent: affirming the consequent instead of the antecedent.
• The fallacy of denying the antecedent: negating the antecedent instead of the consequent.
• False Hypothetical Syllogism: if two different antecedents share a common consequent, it does not mean the two antecedents are the same or identical.

### Comparing Valid and Invalid Forms

• Comparing valid and invalid forms: Modus Ponens vs. affirming the consequent, Modus Tollens vs. denying the antecedent, and Hypothetical Syllogism vs. False Hypothetical Syllogism.

### Validity and Soundness of a Deductive Argument

• Validity vs. soundness of a deductive argument: valid deductive arguments with true premises are sound.

### Contrasting Deduction and Induction

• Deduction moves from general premises to particular conclusions, while induction moves from particular to general.
• Deduction is topic-neutral, while induction depends on subject matter.

### Understanding Particular vs General Statements

• Every statement has two parts: the reference class and the attribute class.
• Particular statements have a specific, countable, and finite reference class (e.g., "That man is a bully").
• General statements have a non-specific, non-countable, and infinite reference class (e.g., "Men are bullies").

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## Description

Explore the concept of syllogisms and how to interpret negations in logical statements. Learn how to determine the positive or negative form of a statement based on its original negation. Enhance your skills in affirming and denying antecedent and consequent.

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