CS 214-01
STUDY GUIDE FOR TEST 1
SPRING 2014
CHAPTER 1.1
Important concepts: propositions, truth tables, tautology, equivalence relations.
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Be able to define and recognize propositions. See Example 1 & Problem 1
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What is a wff?
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Truth tables for basic connective (and, or, implication, equivalence, negation). See Table 1.4
o Be sure you understand what it means to say A ↔ B
o Understand negation of compound statements. See Example 3, Table 1.6
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Tautology versus contradiction.
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DeMorgan’s laws
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Practice 7
CHAPTER 1.2
Important concepts: propositional logic and valid arguments, proof sequences, derivation rules
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Definition of valid argument: page 22
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Be able to apply the derivation rules of propositional logic (Table 1.12, Table 1.13, table 1.14). You don’t need to
memorize the rules, just be able to apply them. I will provide a copy of anything you will need.
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Practice 9, Practice 11, Problem 10 (page 32)
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Be able to recast a verbal argument symbolically and apply the rules to determine whether the
argument is true or false. See Example 18 for an illustration of what you should be able to do.
CHAPTER 1.3
Important Concepts: predicates, quantifiers, domain of interpretation

Be able to state the differences between propositions and predicates.
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What is the predicate characteristic that is an analog to tautology for propositional wff’s? Answer: validity – Be able to
define it.
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Practice 19 – converting English language statements to predicate wffs using quantifiers
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Practice 20 - negation of predicates
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Problem 2
CHAPTER 2.1
Important Concepts: proof techniques, inductive versus deductive reasoning

Disproof by counterexample
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Table 2.2 – other proof methods

Be able to define important terms
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Inductive reasoning leads to conjectures, deductive reasoning proves (or disproves)
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Practice 3, Problems 19, 49.
CHAPTER 2.2
Important concepts: Mathematical induction, primarily the first principle.

Terminology: what is the basis step, etc.
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Example 14, Practice 7, Example 18, Problem 1
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Review Section at end of section
Chapter 2.4

What is a recursive definition?
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When given a definition of a recursively defined sequence be able to generate terms in the sequence
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Know how to define the Fibonacci sequence (Example 30)

Recursive definition of wff’s and Practice 14.

What is a recursive function?
Chapter 2.5
Important concepts: terminology: closed-form solution, linear first-order recurrence relations

Be able to describe the expand, guess, and verify approach to solving recurrence relations
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Practice 21
We’ll work problems in class on Monday and I’ll give you ideas about the kinds of questions that will be on the test