Mastering Discrete Structures and Sets

1. Discrete StructuresCS 23022 Johnnie Baker jbaker@cs.kent.edu Comments on Early Term Test

2. Comments on Early Term Exam • Know truth tables for the basic constructs: and, or, implies, equivalence, exclusive or, biconditional, etc. • Be able to calculate the truth table for compound statements. • Understand standard terminology: contrapositive, converse, tautology, contridiction, • Know the various logical equivalences: See Table 6-8 in section 1.2 • Know meaning and equivalences involving  and  (universal quanifiers.) and how to negate these quantifiers. • Be able to translate logic statements into English statements without variables and symbols. Conversely, be able to translate English statements into logic statements. • Be able to verify correctness of reasoning involving logic statements. • Also, be able to deduce conclusions from logic statements

3. Be able to negate nested quantifiers. • Understand terminology like argument, valid, premises, fallacies, etc. • Know and be able to use the various rules of inferences, such as those in Table 1 on pg 66. • Be able to use the rules of inference to make logical arguments, as in Section 1.5. • Look over added, suggested study odd-nr problems for Section 1.5, as no assignment was made for this section: 3,9,13,15,19,23,27,29,31. • Understand how to work with universal and exitential generalizations and instantiations. • Be able to verify validity of arguments and make arguments involving these concepts. • In section 1.6, understand the terminology concerning mathematical proofs such as theorems, axioms/postulates, proof, etc.

4. In Section 1.6, understand the various methods of proving theorems. • Be able to use the various methods for proving theorems to establish correctness of mathematical statements. • Also, be able to identify errors in the proof of mathematical or logic arguments. • Be able to establish show a mathematical statement is false using a counterexample. • Understand mathematical terminology introduced in material covered, such as integer, rational, irrational, odd, even, • Know the difference between constructive and non-constructive proofs.

5. Sets • Understand set terminology such as set builder notation, and be able to use it. • Know meaning of standard sets like N, Z, Q, R, • Understand standard set theory terminology, e.g., element, subset, cartesian product, universal set, set difference, etc. • Know standard set operations and be able to use them. • Know the standard set identities such as Table 1 on pg 124. • Be able to prove set identities such as (AB)’ = A’  B’, and give reasons for all steps. • Be able to use a truth table to establish set identities.