Midterm 1 Study Guide

Topics:

1. Propositional logic
   • propositional variables
   • logical operators
   • truth tables
   • tautologies and contradictions
   • conditionals (and their contrapositives/inverses/converses)
   • biconditionals
   • logical equivalences
2. Predicate logic
   • predicates as propositional functions
   • quantifiers (universal and existential) and domains
     • negation and nesting
   • translating English to/from logic
   • validity and satisfiability
3. Proofs and Rules of Inference
   • proof: definition
   • rules of inference
   • building valid arguments
   • elementary methods of proof
4. Sets, Functions, and Relations
   • definitions of above
   • set builder notation
   • set membership test
   • empty set
   • fixed set names for numbers
   • set cardinality and countability
   • set operations
   • set identities
   • [proper] subset/superset definitions
   • power set
   • cartesian products
   • relations between/on sets
   • matrix and digraph representation of relations
   • symmetric, antisymmetric, transitive, and equivalence relations
   • types of functions (injection/surjection/bijection/partial)
   • function compositions
   • n-ary relations
   • relational database model