Learning Objectives
Organize Sets and Use Sets to Describe Relationships
- Describe memberships of sets, including the empty set, using proper notation, and decide whether given items are members and determine the cardinality of a given set
- Perform the operations of union, intersection, complement, and difference on sets using proper notation
- Describe the relations between sets regarding membership, equality, subset, and proper subset, using proper notation
- Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems
- Recognize when set theory is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others
Introduction to Logic
- Combine sets using Boolean logic, using proper notations
- Use statements and conditionals to write and interpret expressions
- Use a truth table to interpret complex statements or conditionals
- Write truth tables given a logical implication, and it’s related statements – converse, inverse, and contrapositive
- Determine whether two statements are logically equivalent
- Use DeMorgan’s laws to define logical equivalences of a statement
Analyzing Arguments With Logic
- Discern between an inductive argument and a deductive argument
- Evaluate deductive arguments
- Analyze arguments with Venn diagrams and truth tables
- Use logical inference to infer whether a statement is true
- Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, false dilemma, circular reasoning, post hoc, correlation implies causation, and straw man arguments