Discrete Mathematics Final Exam Outline PDF

Discrete Mathematics Outline for Final Exam ________________________________________________________________________________________ Logic Determine truth tables for compounded statements, and for statements containing conditional and...

Discrete Mathematics Outline for Final Exam ________________________________________________________________________________________ Logic Determine truth tables for compounded statements, and for statements containing conditional and bi- conditional connectives. Determine whether an argument is valid or invalid. State the Law of Inference that supports validity when an argument is valid. Give the input/output table for the following gates: OR, AND and NOT, find a Boolean expression of a circuit, and find a circuit corresponding to a Boolean circuit. Reduce a circuit to a circuit with less gates. Identify universal conditional statements. Negate universal statements, existential statements, and statements containing two different quantifiers. Identify the converse, inverse and converse of a given conditional statement. Direct and Indirect Proofs Make sure you know the formal definitions for: Odd and Even Integers, Rational Numbers, Divisibility and the QRT. Use direct proofs or counterexamples to prove or disprove statements involving the odd/even numbers. Use direct proofs or counterexamples to prove or disprove statements involving the rational numbers. Use direct proofs or counterexamples to prove or disprove statements involving the divisibility of integers, and use the quotient-remainder theorem to illustrate a proof by division into cases. Use methods of proofs by contradiction and contraposition to prove various statements. Sequences Do calculations involving factorial, summation and product notations. Prove statements using mathematical induction. Sets Determine the union, intersection, difference and complement of sets and intervals of real numbers, illustrate sets using Venn diagrams. Prove set identities using element argument. Prove set identities algebraically. Use contradiction to prove various statements involving sets Functions Know the formal definition of 1-1 and onto functions. Prove or disprove whether a function is one-to-one. Prove or disprove whether a function is onto. Know the composition of two given functions. Determine if a function is bijection, and if so find the inverse function. Relations Determine the directed diagram of a relation on a finite set. Determine (prove) if a relation on a finite or infinite set is reflexive, symmetric or transitive. Graphs Determine if a given set of vertices with specific degrees determine a graph. If so, sketch the graph. Determine whether a given graph has an Euler circuit and, if so, indicate one. Determine whether a given graph has an Euler path and, if so, indicate one. Review Problems for Final Exam 1. Go over your writing assignments and look at your mistakes. Sometimes I upload attachments to your account. You need to click on the assignment in order to access the attachment that has feedback on it. 2. Here is a list of problems from the textbook for additional practice. 2.1 3, 5, 9, 13, 23, 25, 29, 33, 35, 37, 49, 51, 53 2.2 5, 11, 13 (make sure you know these laws), 19, 21, 22, 23, 24, 25, 26, 27, (use logical equivalence to prove 29, 31), 33, 41, 43, 45 2.3 24-23 (it will help to symbolize each argument first) 2.4 3, 7, 11, 19, 27, 29, 31 3.1 5, 9, 11, 15, 19, 23, 33 3.2 9, 15, 17, 19, 21, 27, 29, 31, 39, 41 3.3 12, 13, 15, 17, 41 4.1 3, 5, 9, 11, 15 4.2 1, 2, 7, 13, 23, 25, 27 4.3 5, 7, 8, 11, 15, 17 4.4 1, 3, 5, 7, 11, 13, 15, 17,19, 24 4.5 7, 9, 17, 19, 21, 23, 25, 27, 29 4.7 3, 5, 7, 13, 21 4.9 3, 7, 9, 17 5.1 29, 31, 43, 47, 52 5.2 3, 6,7, 10, 11, 13 5.3 9, 10, 11, 12 6.1 3, 5, 9, 11, 17 6.2 7, 9, 11, 16,18, 19 6.3 27, 29, 31, 32, 33, 34, 35 7.1 2, 8, 9, 13 7.2 1, 7, 11, 13, 15, 46, 47 7.3 3, 5, 7 8.1 5, 6, 16, 18 8.2 9, 10, 11, 13, 15, 18, 19, 32, 33 10.1 8, 9, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22