Learning Outcomes At the end of this course, students should be able to:
convert logical statements from informal language to propositional and predicate logic expressions;
describe the strengths and limitations of propositional and predicate logic;
outline the basic structure of each proof technique (direct proof, proof by contradiction, and induction) described in this unit;
apply each of the proof techniques (direct proof, proof by contradiction, and induction) correctly in the construction of a sound argument;
apply the pigeonhole principle in the context of a formal proof.;
compute permutations and combinations of a set, and interpret the meaning in the context of the particular application;
map real-world applications to appropriate counting formalisms, such as determining the number of ways to arrange people around a table, subject to constraints on the seating arrangement, or the number of ways to determine certain hands in cards (e.g., a full house); and