a. What are primitive terms?2. Give truth tables
b. What are axioms?
c. Give an example of an axiom.
d. Give the primitive terms in your example of an axiom.
e. What is the difference between a conjecture and a theorem?
a. Give the hypothesis4. Give a Venn diagram representing A and B.
b. Give the conclusion.
5. Direct proofs
a. Describe the concept of a direct proof.6. What is a syllogism?
b. Prove a statement using direct proof.
a. Give an example8. Contrapositive
c. Give the conclusion given the premises of a syllogism.
a. Define contrapositive9. Prime numbers
b. Prove, using a truth table, that a statement and its contrapositive are equivalent
c. Give a proof of a statement by proving its contrapositive.
d. Give the contrapositive of a statement.
a. Define prime numbers10. Proof by contradiction
b. Determine if a number is prime.
c. Give the prime factorization of a number
a. What is the principle of proof by contradiction?11. Qualified Statements
b. Why does proof by contradiction work?
c. Prove that there is no largest prime number
d. Prove that the square root of a number is irrational
e. Prove that the cube root of a number is irrational
f. Show why the proof technique of part d does not work if the number is a perfect square.
a. Be able to express a qualified statement in symbols.12. Mathematical Induction
b. Be able to give the negation of qualified statements
a. Understand the concept of summation.
b. Be able to define the principle of mathematical induction
c. Give proofs of summation formulas using mathematical induction