Exam (elaborations)
C959 Flashcards (Master set) questions and answers.
- Course
- Institution
C959 Flashcards (Master set) questions and answers.
[Show more]
Seller
Follow
GUARANTEEDSUCCESS
Reviews received
Content preview
C959 Flashcards (Master set) questionsand answers
Proof by Exhaustion - answer Prove the statement by checking each element individually. Unlike proof by
cases, exhaustive proof looks at every case in a way that is not general.
Proof by Counterexample - answer Used to disprove a universal statement. For example, to disprove the
statement, "All prime numbers are odd" find one example where this statement is false—the number 2
—which is both even and prime.
Direct Proof - answer In the direct proof, we assume the hypothesis p is true and we try to prove that q is
true. Thus making p→q true.
Proof by Contrapositive - answer A proof that makes use of the fact that p→q is equivalent to its
contrapositive ¬q→¬p. So we assume that ¬q is true and try to prove that ¬p is true.
Proof by Contradiction - answer An indirect proof where if the theorem being proven has the form p →
q, then the beginning assumption is p ∧ ¬q which is logically equivalent to ¬(p → q).
Proof by Cases - answer In proof by case, we are looking at all the possible cases that might arise in a
theorem.
∴ - answer Means "therefore".
Conditional Statements - answer If p then q. p → q. Only not true when p is true and q is false. It breaks
the contract.
Converse - answer Converse of p → q is q → p.
Contrapositive - answer Contrapositive of p → q is ¬q → ¬p.
, Inverse - answer Inverse of p → q is ¬p → ¬q.
Biconditional Statement - answer p if and only if q. p ↔ q. True when p and q have the same truth value
(including False ↔ False) and is false when p and q have different truth values.
Logical Equivalence - answer p is logically equivalent to q. p ≡ q. Logically equivalent if they have the
same truth value regardless of the truth values of their individual propositions. So p ≡ ¬¬p or ¬p ≡ p →
¬q.
Logical Operator - answer Conjunction — p ∧ q. True only if p and q are true.
Disjunction — p ∨ q. True when either of p or q, or both is true.
Exclusive or — p ⊕ q. True if either one of p or q is true but not both.
Negation — ¬p. Negates value. If True then not True, if False then not False.
Order of Operations - answer 1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
4. →
5. ↔
Predicate - answer Logical statement whose truth value is a function of one or more variables.
Free Variable - answer Variable is free to take on any value in the domain. In (∀x P(x)) ∧ Q(x), Q(x) is the
free variable.
Bound Variable - answer Variable is bound to a quantifier. In (∀x P(x)) ∧ Q(x), P(x) is the bound variable.
DeMorgan's Laws for Quantifiers - answer ¬∀ x F(x) as "Not every bird can fly." Which is logically
equivalent (≡) to ∃ x ¬ F(x) as "There exists a bird that cannot fly."
¬∃ x Q(x) as "It is not true that there is a child in the class who is absent today." Which is logically
equivalent (≡) to ∀ x ¬ Q(x) as "Every child in the class is not absent today."
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller GUARANTEEDSUCCESS. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $12.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now