1. 1 Discrete Structures CS 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 2

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. 3

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. 4

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. 5