Essential Ideas

Section 3.2: Truth Tables and the Conditional

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3.2 Outline

  1. Constructing truth tables
    1. fundamental operators (and, or, and not )
    2. truth table
    3. law of double negation
  2. Conditional
    1. translation: if p, then q
    2. antecedent
    3. consequent
    4. uses
    5. definition
  3. Translations for the conditional
    1. converse
    2. inverse
    3. contrapositive
    4. law of
… See the whole entry

Section 3.1: Deductive Reasoning

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3.1 Outline

  1. Terminology
    1. argument
    2. hypotheses/premises
    3. deductive reasoning
    4. valid
    5. logic
    6. symbolic logic
    7. statement
    8. simple statement
    9. operators (connectives)
    10. compound statement
    11. fuzzy logic
    12. law of the excluded middle
    13. truth value of a simple statement
  2. Conjunction
    1. translation: and
    2. definition
  3. Disjunction
    1. translation: or
    2. definition
  4. Negation
… See the whole entry

Section 2.4: Finite and Infinite Sets

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2.4 Outline

  1. Infinite sets
    1. finite
    2. infinite
    3. one-to-one
    4. correspondence
    5. countable/uncountable
      1. rational numbers are countable
      2. real numbers are uncountable
  2. Cartesian product of sets
    1. definition
    2. cardinality of a Cartesian product
    3. fundamental counting principle

2.4 Essential Ideas

One-to-one Correspondence

Two sets A and B… See the whole entry

Section 2.1: Sets, Subsets, and Venn Diagrams

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2.1 Outline

  1. Denoting sets
    1. undefined term; set
    2. circular definition
    3. specifying sets
      1. description method
      2. roster method
    4. well-defined set
    5. terms
      1. members
      2. elements
      3. belong to
      4. contained in
    6. Sets of numbers
      1. natural numbers
      2. counting numbers
      3. integers
      4. rational numbers
    7. set-builder notation
  2. Equal and equivalent sets
… See the whole entry

Section 1.4: Review for Chapter 1

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Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 1.

Addition law of exponents [1.3]… See the whole entry

Section 1.3: Scientific Notation and Estimation

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1.3 Outline

  1. Exponential notation (see below)
    1. base
    2. exponent
    3. power or exponential
    4. extended order of operations
  2. Scientific notation (see below)
  3. Calculators
    1. arithmetic logic
    2. algebraic logic
    3. RPN logic
    4. floating-point form
  4. Estimation
  5. Laws of exponents (see below)
    1. addition law
    2. multiplication law
    3. subtractive law
… See the whole entry