# Midterm 1 Study Guide

Topics:

1. Propositional logic
• propositional variables
• logical operators
• truth tables
• 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