Logic - Deductive, Non-deductive, Reductio, Contradiction

What is a deductive argument?

• An argument where the conclusion is likely
• An argument where the conclusion follows necessarily
• An argument based on probability
• An argument that refutes itself

Answer explanation

A deductive argument ensures that if the premises are true, the conclusion must also be true.

What is a premise in an argument?

• A statement used as a basis for an argument
• A statement that must be true
• A rhetorical question
• A conclusion drawn from evidence

Answer explanation

A premise is a foundational statement in an argument that provides support for the conclusion.

What does it mean if an argument is valid?

• The premises are true
• The conclusion is true
• The conclusion logically follows from the premises
• The argument is persuasive

Answer explanation

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

What makes an argument sound?

• The argument is persuasive
• The argument has valid reasoning
• The conclusion is true
• The argument is valid and the premises are true

Answer explanation

A sound argument is both valid and has all true premises, ensuring the truth of the conclusion.

Which of the following best describes a non-deductive argument?

• An argument where the conclusion is probable
• An argument with a true conclusion
• An argument with valid premises
• An argument that refutes itself

Answer explanation

Non-deductive arguments suggest that the conclusion is likely but not guaranteed.

What is proof by contradiction?

• A method of finding a contradiction
• Proving a statement by assuming the opposite and deriving a contradiction
• Proving the truth of a theorem
• A method of validating a conjecture

Answer explanation

Proof by contradiction assumes the negation of a statement and shows it leads to a contradiction, thus proving the original statement true.

What is a conjecture?

• A statement proposed without proof
• A proven statement
• A hypothesis
• A logical contradiction

Answer explanation

A conjecture is a proposition that is assumed true but has not yet been proven.

Which of the following is an example of reductio ad absurdum?

• Assuming a claim is true and showing it leads to a contradiction
• Providing evidence for a claim
• Showing a claim is false
• Proving a statement by analogy

Answer explanation

Reductio ad absurdum involves proving the falsity of a proposition by showing that its logical consequence is absurd or contradictory.

In logic, what is a theorem?

• A statement that has been proven to be true
• A statement that is assumed to be true
• A statement that is likely true
• A statement that contradicts itself

Answer explanation

A theorem is a mathematical statement that has been proven based on previously established statements.

What is the role of a conclusion in an argument?

• The statement that the premises support
• The starting point of an argument
• The evidence for a premise
• A rhetorical question

Answer explanation

The conclusion is the statement that logically follows from the premises in an argument.