 ```Discrete Structures
CS 23022
Johnnie Baker
[email protected]
1
• 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
• 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
• 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
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
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