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Validity Of Arguments Quiz 9 (10 MCQs)

This set of multiple-choice questions evaluates logical reasoning skills, focusing on the existence of a first cause, infinite regress, and necessary vs. contingent beings. It assesses the ability to analyze argument validity, soundness, and the use of counterexamples to disprove statements. Concepts such as deductive arguments, logical form, and the truth of conclusions are also covered.

Quiz Instructions

Select an option to see the correct answer instantly.

1. If an argument's premises are true and the argument is valid, what can we say about the conclusion?

Correct Answer: Correct answer is: (B) It is necessarily true.

Exam Relevance: GRE, LSAT, GMAT, Philosophy Exams

Difficulty: Moderate

Concept notes: In the context of argument validity, if the premises of an argument are true and the argument is valid, the conclusion must be true. This is a fundamental principle of logical reasoning.

Common Mistakes: A common misunderstanding is that validity alone guarantees the truth of the conclusion. However, validity only ensures that if the premises are true, the conclusion must be true. The truth of the premises is also crucial.

Explanations: An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. Therefore, if the premises are true and the argument is valid, the conclusion must be true. This is why the correct answer is that the conclusion is necessarily true.

Option Analysis:

Option A: Soundness requires both validity and true premises, but the question only asks about the conclusion's truth given valid premises. Soundness is not directly relevant here.
Option B: This is correct because if the premises are true and the argument is valid, the conclusion must be true.
Option C: Proof implies a rigorous demonstration of truth, which is not the same as the necessary truth of a conclusion in a valid argument with true premises.
Option D: Cogency is a term used in inductive reasoning, not in the context of deductive validity.

2. The universe is therefore also contingent, so at one point nothing existed. This means there must be a .....

Correct Answer: Correct answer is: (A) Necessary being.

Exam Relevance: Philosophy exams, Theology exams, Logic exams

Difficulty: Moderate

Concept notes: The concept of a necessary being is central to arguments about the existence of a first cause or ultimate explanation for the universe. A necessary being is one that must exist and cannot not exist, in contrast to a contingent being, which may or may not exist.

Common Mistakes: A common misunderstanding is to confuse a necessary being with a contingent being, which is dependent on other factors for its existence.

Explanations: The argument presented suggests that the universe is contingent, meaning it could have not existed. If the universe is contingent, it must have a cause. This cause cannot itself be contingent, as that would lead to an infinite regress of contingent causes. Therefore, there must be a necessary being, one that exists by its own nature and does not depend on anything else for its existence.

Option Analysis:

Option A: Correct. A necessary being is required to break the chain of contingent causes.
Option B: Incorrect. A contingent being is dependent on other factors and cannot be the ultimate cause.
Option C: Incorrect. While an uncaused causer is a related concept, it does not specifically address the necessity of the being.
Option D: Incorrect. An unmoved mover is a concept from Aristotelian philosophy and does not directly address the necessity of the being.

3. Which of these is a counterexample to the following statement?If a number is divisible by 3 then it is odd.

Correct Answer: Correct answer is: (B) 6.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Easy

Concept notes: A counterexample to a statement is an example that disproves the statement. In this case, the statement is "If a number is divisible by 3 then it is odd." A counterexample would be a number that is divisible by 3 but is not odd.

Common Mistakes: A common mistake is to assume that all numbers divisible by 3 are odd, which is not true.

Explanations: The number 6 is divisible by 3 (since 6 ÷ 3 = 2) but it is not an odd number (since it is even). Therefore, 6 is a counterexample to the statement "If a number is divisible by 3 then it is odd."

Option Analysis:

Option A: 3 is divisible by 3 and is odd, so it does not disprove the statement.
Option B: 6 is divisible by 3 but is not odd, so it disproves the statement.
Option C: 8 is not divisible by 3, so it is not relevant to the statement.
Option D: 11 is not divisible by 3, so it is not relevant to the statement.

Mnemonic: Divisible by 3, even number, counterexample.

4. All insects are animals.A butterfly is an insect.Therefore, a butterfly is an animal.

Correct Answer: Correct answer is: (A) Valid and Sound.

Exam Relevance: GRE, LSAT, GMAT

Difficulty: Easy

Concept notes: An argument is valid if the conclusion logically follows from the premises. An argument is sound if it is valid and all its premises are true.

Common Mistakes: A common mistake is to confuse validity with soundness. An argument can be valid but unsound if the premises are false.

Explanations: The argument is valid because the conclusion logically follows from the premises. The premises are: 1. All insects are animals. 2. A butterfly is an insect. The conclusion is: 3. Therefore, a butterfly is an animal. Since the premises are true and the conclusion logically follows, the argument is also sound.

Option Analysis:

Option A: Correct. The argument is both valid and sound.
Option B: Incorrect. The argument is not unsound because the premises are true.
Option C: Incorrect. The argument is valid, so it cannot be invalid.
Option D: Incorrect. The argument is valid and sound, so it cannot be invalid and unsound.

Mnemonic: Valid = Viable, Sound = True

5. Is this argument valid or invalid (if invalid, what fallacy is it using)?Premise 1: Homework is fun.Premise 2: I do homework every day.Premise 3: I have fun when I do homeworkConclusion: I have fun every day.

Correct Answer: Correct answer is: (A) Valid.

Exam Relevance: GRE, LSAT, GMAT

Difficulty: Moderate

Concept notes: An argument is valid if the conclusion logically follows from the premises, regardless of the truth of the premises.

Common Mistakes: A common mistake is to assume that the argument is invalid because the premises might not be true in reality. However, validity is concerned with the logical structure, not the factual accuracy of the premises.

Explanations: The argument is valid because the conclusion logically follows from the premises. Premise 1 states that homework is fun, Premise 2 states that the individual does homework every day, and Premise 3 states that the individual has fun when doing homework. Therefore, the conclusion that the individual has fun every day logically follows from these premises.

Option Analysis:

Option A: The argument is valid because the conclusion logically follows from the premises.
Option B: The argument is not a straw man fallacy because it does not misrepresent or exaggerate any position.
Option C: The argument is not making it personal because it does not attack the individual's character or personal traits.
Option D: The argument is not a false dilemma because it does not present a limited set of options as the only possibilities.

6. Which of the following equations shows the correct use of counter-example for the statement "The sum of two integers is always positive" ?

Correct Answer: Correct answer is: (C) $-25+14=-11$.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: A counter-example is a specific instance that disproves a general statement. In this case, the statement is "The sum of two integers is always positive." A counter-example would be a pair of integers whose sum is not positive.

Common Mistakes: A common mistake is to choose an example where the sum is positive, which does not disprove the statement. Another mistake is to choose an example where the sum is zero, which does not strictly disprove the statement as zero is not positive.

Explanations: The correct answer is $-25+14=-11$ because it provides a specific example where the sum of two integers is not positive. This counter-example disproves the statement "The sum of two integers is always positive."

Option Analysis:

Option A: $10+24=34$ is a positive sum, which does not disprove the statement.
Option B: $-5+20=15$ is a positive sum, which does not disprove the statement.
Option C: $-25+14=-11$ is a negative sum, which disproves the statement.
Option D: $8+9=17$ is a positive sum, which does not disprove the statement.

7. This is used to prove that a possible Conditional Statement is false.

Correct Answer: Correct answer is: (A) Counterexample.

Exam Relevance: GRE, LSAT, GMAT, SAT

Difficulty: Easy

Concept notes: A counterexample is a specific instance that disproves a general statement or conditional statement.

Common Mistakes: A common misunderstanding is that inductive reasoning or negation can be used to disprove a conditional statement, but these methods do not provide a concrete example to disprove the statement.

Explanations: A counterexample is used to disprove a conditional statement by providing a specific instance where the hypothesis is true but the conclusion is false. This directly shows that the conditional statement is not universally true.

Option Analysis:

Option A: Correct. A counterexample is used to disprove a conditional statement by providing a specific instance where the hypothesis is true but the conclusion is false.
Option B: Incorrect. Inductive reasoning is used to make generalizations based on specific observations, not to disprove a conditional statement.
Option C: Incorrect. A concluding statement is the result of a logical argument, not a method to disprove a conditional statement.
Option D: Incorrect. Negation is the opposite of a statement, but it does not provide a specific instance to disprove a conditional statement.

8. (Analysis) If an argument has a true conclusion but doesn't follow from premises, it is:

Correct Answer: Correct answer is: (C) Invalid.

Exam Relevance: GRE, LSAT, GMAT, Philosophy Exams

Difficulty: Moderate

Concept notes: An argument is considered valid if the conclusion logically follows from the premises, regardless of the truth of the premises or the conclusion. If the conclusion is true but does not logically follow from the premises, the argument is invalid.

Common Mistakes: A common misunderstanding is that an argument is valid if its conclusion is true. However, validity is solely about the logical relationship between the premises and the conclusion.

Explanations: An argument is valid if the truth of the premises guarantees the truth of the conclusion. If the conclusion is true but does not logically follow from the premises, the argument is invalid. Therefore, an argument with a true conclusion that does not follow from the premises is invalid.

Option Analysis:

Option A: An argument is valid if the conclusion logically follows from the premises, not just because the conclusion is true.
Option B: The truth of the conclusion does not determine the validity of the argument. An argument can have a true conclusion and still be invalid.
Option C: An argument is invalid if the conclusion does not logically follow from the premises, even if the conclusion is true.
Option D: An argument's validity is not related to it being a general law. Validity is about the logical relationship between premises and conclusion.

9. When we rebut, we must show that the opposition arguments are .....

Correct Answer: Correct answer is: (D) Invalid.

Exam Relevance: GRE, LSAT, GMAT

Difficulty: Moderate

Concept notes: When rebutting an argument, the goal is to demonstrate that the argument is not logically sound or does not hold up to scrutiny. This involves showing that the argument is invalid, meaning it does not follow a valid logical structure or its premises do not support its conclusion.

Common Mistakes: A common misunderstanding is that rebutting an argument involves showing that the argument is irrelevant or poorly constructed, rather than focusing on the logical validity of the argument.

Explanations: Rebutting an argument requires demonstrating that the argument is invalid. An argument is considered invalid if its conclusion does not logically follow from its premises, regardless of whether the premises are true or false. By showing that the argument is invalid, one effectively undermines the opposition's position.

Option Analysis:

Option A: Logic refers to the structure and reasoning of an argument, but rebutting requires showing that the argument is invalid, not just logical.
Option B: Relevance is important for the context of the argument, but rebutting specifically targets the logical validity of the argument.
Option C: Well-constructed arguments are those that are logically sound, but rebutting involves showing that the argument is not logically sound.
Option D: Invalid means the argument does not follow a valid logical structure, which is the goal when rebutting an argument.

10. The validity of a deductive argument is determined based on its form and the truth of its premises or conclusion.

Correct Answer: Correct answer is: B) False.

Exam Relevance: GRE, LSAT, GMAT

Difficulty: Moderate

Concept notes: The validity of a deductive argument is determined solely by its logical form, not by the truth of its premises or conclusion.

Common Mistakes: A common misunderstanding is that the truth of the premises or conclusion is necessary to determine the validity of a deductive argument.

Explanations: A deductive argument is valid if and only if the conclusion necessarily follows from the premises, regardless of whether the premises or conclusion are actually true. The validity of a deductive argument is a matter of logical form, not the factual accuracy of the premises or conclusion.

Option Analysis:

Option A: This option is incorrect because the validity of a deductive argument is not determined by the truth of its premises or conclusion, but by its logical form.
Option B: This option is correct because the validity of a deductive argument is determined solely by its logical form, not by the truth of its premises or conclusion.

Frequently Asked Questions

What is the definition of a valid argument?

A valid argument is one where if the premises are true, the conclusion must also be true. The logical structure ensures that the conclusion follows necessarily from the premises.

How can I determine if an argument is valid?

To determine if an argument is valid, examine its logical form and structure. If the conclusion logically follows from the premises, the argument is valid. Counterexamples can be used to show invalidity.

What is the difference between a valid argument and a sound argument?

A valid argument has a structure where true premises lead to a true conclusion. A sound argument is both valid and has all true premises. Thus, a sound argument guarantees a true conclusion.

How do premises and conclusions relate in logical reasoning?

In logical reasoning, premises provide the foundational statements or evidence, while the conclusion is the statement that follows from the premises. The logical relationship between them determines the argument's validity.

What is a counterexample in the context of logical reasoning?

A counterexample is a specific instance that disproves a general statement or argument. It demonstrates that the argument is invalid by showing a case where the premises are true but the conclusion is false.

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