Test 2 Review Information
Test 2 is on Tuesday (11/9) in class. It will be closed book and notes, except you will be allowed to bring your yellow sheet of Logic Rules and one other sheet of paper (8.5" x 11") with notes (on both sides).
Below are the hightlights of each section:
Topics: Exhaustive proof, Inductive reasoning, deductive reasoning, contrapositive, counterexample
Be able to find a counterexamples to prove something is not true
Be able to construct an exhaustive proof
Be able to construct a direct proof
Be able to perform a proof by contraposition
Be able to perform a proof by contradiction
Topics: First Principle of Mathematical Induction, Second Principle of Mathematical Induction
Be able to perform a proof using the First Principle of Mathematical Induction
Be able to perform a proof using the Second Principle of Mathematical Induction
Topics: Definitions of sets, set operations (union, intersection, complement, cross product), power set.
Standard sets: etc.
Describe a set by listing elements and by a characteristic property.
Prove that one set is a subset of another
Find the power set of a set
Check that the required properties for a binary and unary operation are satisfied.
Prove set identities by showing set inclusion in each direction or using the basis set identities.
Topics: Decision Trees, Multiplication Principle, Addition Principle, combining the Multiplication and Addition Principles
Be able to count the number of outcomes
Topics: Principle of Inclusion and Exclusion, Pigeonhole Principle
Be able to find the number of elements in the union of sets using the Principle of Inclusion and Exclusion.
Be able to find the minimum number of elements in a set to guarantee two elements with the same property.
Topics: Permutation, Factorial, Combination
Find the number of permutations of r distinct objects chosen from n distinct objects.
Find the number of combinations of r distinct objects chosen from n distinct objects.
Use permutations and combinations in conjunction with the Multiplication Addition Principles.
Find the number of permutations of n objects that are not all distinct.
Find the number of permutations of r objects out of n distinct objects when objects may be repeated.
Find the number of combinations of r objects out of n distinct objects when objects may be repeated.
Topics: Probability, Probability Distributions, Conditional Probability, Expected Value, Average Case Analysis of Algorithms
Compute the probability when all outcomes are equally likely.
Compute the probability when a probability distribution has been assigned to the sample space.
Compute the conditional probability of an event given that another event has already occurred.
Determine whether two events are independent.
Compute expected value given a sample space with a random variable X and a probability distribution.
Compute the average case analysis of an algorithm.