MTH401

1. What is the conclusion of a proof?

a) The statement being proven b) The assumptions of the proof c) The logical reasoning used in the proof d) The definition of key terms in the proof

2. Which of the following is an example of a vacuous proof?

a) Proving that 2+2=5 b) Proving that all even numbers are divisible by 3 c) Proving that there are no unicorns d) Proving that all odd numbers are prime

3. Which proof strategy involves assuming the negation of the statement being proven and deriving a contradiction?

a) Direct proof b) Proof by contraposition c) Proof by contradiction d) Proof of equivalence

4. Which of the following is an example of a counterexample?

a) Proving that all prime numbers are odd b) Proving that all cats have fur c) Proving that all functions are continuous d) Showing that 2 is not a solution to the equation x^2=3x

5. Which of the following is an example of a trivial proof?

a) Proving that 2+2=4 b) Proving that all prime numbers are odd c) Proving that all even numbers are divisible by 3 d) Proving that all cats have fur

6. Which proof strategy involves showing that the statement being proven is false by finding a specific example that contradicts it?

a) Direct proof b) Proof by contraposition c) Proof by contradiction d) Proof by counterexample

7. Which of the following is an example of a mistake in a proof?

a) Starting with false assumptions b) Using valid logical reasoning c) Using a proof by contradiction d) Deriving the correct conclusion

8. What is the hypothesis of a proof?

a) The statement being proven b) The assumptions of the proof c) The logical reasoning used in the proof d) The definition of key terms in the proof

9. Which proof strategy involves showing that if the negation of the statement being proven is true, then a contradiction arises?

a) Direct proof b) Proof by contraposition c) Proof by contradiction d) Proof of equivalence

10. Which of the following is a valid propositional equivalence?

a) p and q = q or p b) p implies q = not p or q c) p xor q = not p and not q d) p or (not q) = not (p and q)

Math MCQs

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