Group 4

1. What is the purpose of proofs in mathematics?

• A) To simplify mathematical statements.

• B) To establish the truth of mathematical statements.

• C) To illustrate mathematical concepts with examples.

• D) To challenge mathematical assumptions.

2. What is meant by an argument?

• A) A sequence of questions that begin with an answer.  

• B} A sequence of premises that end without a conclusion.  

• C) A sequence of statements that end with a conclusion.  

• D) A sequence of unrelated sentences.

3. What does it mean for an argument to be valid?

• A) The premises and conclusion are all true.

• B) The conclusion logically follows from the premises.

• C) The argument has convincing premises.

• C) The argument has convincing premises.

4. Which of the following represents a basic tool for establishing the truth of statements?

• A) Rules of inference  

• B) Rules of deduction  

• C) Rules of induction  

• D) Rules of speculation  

5. What are rules of inference used for in logical reasoning?

• A) To create new templates for constructing arguments  

• B) To deduce new statements from existing statements  

• C) To validate existing arguments without constructing new ones  

• D) To provide examples of invalid arguments

6. Which symbol denotes "therefore"?

• A) ∅

• B) ∠

• C) ∴

• D) ∞

7. Which of the following best describes the concept of a valid argument?

• A) An argument is valid if its premises are false but the conclusion is true.

• B) An argument is valid if its conclusion is false regardless of the truth value of its premises.

• C) An argument is valid if its premises and conclusion are all true simultaneously.

• D) An argument is valid if whenever all its premises are true, the conclusion must also be true.

8. Which term refers to the final proposition in an argument?

• A) Conclusion

• B) Premise

• C) Hypothesis

• D) Assumption

9. Which term refers to the statements that serve as the foundation of an argument?

• A) Premises

• B) Conclusion

• C) Propositions

• D) Assumptions

10. Which logical rule of inference is based on the tautology (p ∧ (p → q)) → q?

• A) Modus Tollens

• B) Hypothetical Syllogism

• C) Modus Ponens

• D) Disjunctive Syllogism