Module 1: Logic and Proofs

Propositional Logic

1. Construct statements using propositional logic.
2. Apply propositional logic to solve real-world problems.

Notes:

• A Proposition is a declarative sentence that is either true or false (lecture notes)
• Use Connectives (Logical Operators) to create compound propositions.
  • Negation ¬ | ¬ p == "not p"
  • Conjunction ∧ | p ∧ q == "p and q"
  • Disjunction ∨ | p ∨ q == "p or q"
    • Or gets interesting, the "inclusive or" [P=T ∨ Q=T == T] is where at least one of the two is true and they are both true, but it doesn't have to be this way. "Exclusive or" (⊕, XOR) ... one or the other but not both... (soup or salad)
  • Implication →

Online Resources:

• Lecture Notes: https://www.cs.odu.edu/~toida/nerzic/content/web_course.html
  • 3 (A & B)
• Understanding Check: http://highered.mheducation.com/sites/dl/free/0073383090/928180/Rosen7eExtraExamples0101.pdf

All images above from: TheTrevTutor on Youtube > https://www.youtube.com/user/thetrevtutor

Equivalences

1. Describe propositional equivalences.

Notes:

Resources:

Quantifiers

1. Compare and contrast predicates and quantifiers.
2. Explain nested quantifiers.

Notes:

Resources: