CMSC56

Question 1

Valid argument that establishes truth
of a theorem

Answer 1

Proofs

Question 2

Statements that can be shown as true
Facts or Results

Answer 2

Theorems

Question 3

Assumed true statements

Answer 3

Axioms

Question 4

“Pre-theorem”. Less important theorems that is
used to prove the theorem

Answer 4

Lemma

Question 5

“Post-theorem”. Theorem that can be established
directly from a theorem that has been proved.

Answer 5

Corollary

Question 6

statement believed to be a true statement, usually on the basis of
some partial evidence, a heuristic argument, or the intuition of an
expert.

Answer 6

Conjecture

Question 7

leads from the hypothesis of the theorem to
the conclusion

Answer 7

Direct Proof

Question 8

are proofs that do not start from the
hypothesis and ends in the conclusion

Answer 8

Indirect Proof

Question 9

p → q ≡ ¬q → ¬p

Answer 9

Proof by Contraposition

Question 10

● Another type of indirect proof
● Negate the hypothesis
● Show that it leads to a contradiction

Answer 10

Proof by Contradiction

Question 11

● Proving if and only if
● (p ↔ q) ↔ (p → q) ∧ (q → p)

Answer 11

Proof by Equivalences

Question 12

● Proving that a statement is false
● Find an element that makes the statement false

Answer 12

Counterexample

Question 13

● Show that the statement is false:
○ “Everyday is a weekday”

■ Saturday and Sundays are weekends

Answer 13

○ Counterexample proof: