CH1 – 3 REVIEW
Summary
Key Terms
Logic
Argument – premises, conclusions
Fallacy
Key Ideas and Skills
Identify an argument’s premises and conclusions.
Recognize fallacious arguments, which contain logical flaws so that
their conclusions are not well supported by their premises
CHAPTER 1: 1A RECOGNIZING FALLACIES
KEY TERMS AND KEY IDEAS AND SKILLS
Key Terms
Proposition
Truth values, truth tables
Negation: not p
Conjunction: p and q
Disjunction: p or q
Conditional: if p, then q
Logical equivalence
1B: PROPOSITIONS AND TRUTH VALUES
KEY TERMS
Understand truth tables for negation, conjunction, disjunction,
conditional.
Inclusive vs. exclusive: Inclusive (or) means either or both;
exclusive or means one or the other, but not both
Variations on the conditional: if p, then q
Converse: if q, then p
Inverse: if not p then not q
Contrapositive: if not q, then not p
1B: PROPOSITIONS AND TRUTH VALUES
KEY IDEAS AND SKILLS
Key
Terms:
Set
Categorical
Propositions
Venn
diagrams
1C: SETS AND VENN DIAGRAMS
KEY TERMS
Set Relationships
Subsets, disjoint sets, overlapping sets
Four categorical propositions
All S are P;
No S are P;
Some S are P;
Some S are not P
Uses of Venn diagrams
Illustrating set relationships
Organizing information
1C: SETS AND VENN DIAGRAMS
KEY IDEAS AND SKILLS
Inductive
argument
Strength
Deductive
argument
Validity
Soundness
ID: ANALYZING ARGUMENTS
KEY TERMS
Evaluating arguments
Inductive arguments in terms of strength
Deductive arguments in terms of validity and soundness
Venn diagram tests of validity
Chains of conditionals
Induction and deduction in mathematics
Propose a theorem inductively
Prove a theorem deductively
1D: ANALYZING ARGUMENTS
KEY IDEAS AND SKILLS
Key Terms
Critical thinking
Key ideas and skills
1. Read (listen) carefully
2. look for hidden assumptions
3. Identify the real issue
4. Understand the options
5. Watch for fine print and missing information
6. Are other conclusions possible
1E: CRITICAL THINKING IN EVERYDAY LIFE
KEY TERMS AND KEY IDEAS AND SKILLS
Key Terms
Units
Conversion factor
Currency conversions
Key ideas and skills
Identify units with key words per, square, or cube or with hyphens
Write conversion factors in three equivalent forms
Work with units to check answers and help solve problems
CHAPTER 2: 2A PROBLEM SOLVING POWER OF UNITS
KEY TERMS AND KEY IDEAS AND SKILLS
US customary system (USCS)
Metric system (SI)
Celsius, Fahrenheit, Kelvin
Absolute zero
Energy units: Calorie, Joule, Kilowatt-hour
Power units: 1 watt = 1 joule/s
Density
Concentration
Blood alcohol
content
2B: MORE PROBLEM SOLVING POWER OF UNITS
KEY TERMS
Understand and convert basic USCS and metric units
Know metric prefixes
Know temperature units and convert between °F, °C, and Kelvin
Understand energy units and power units
Energy is what makes matter move or heat up
Power is the rate at which energy is used
Apply the concept of density to materials, population, and
information
Apply the concept of concentration to pollution and blood
alcohol content
2B: MORE PROBLEM SOLVING POWER OF UNITS
KEY IDEAS AND SKILLS
Key
Terms
Four-step
Key
problem-solving process
ideas and skills
Apply
eight strategic hints for problem
solving
2C: PROBLEM-SOLVING GUIELINES AND HINTS
KEY TERMS AND KEY IDEAS AND SKILLS
Key
ideas
Absolute
Relative
Change
Absolute
Relative
change
difference
difference
3A: USES AND ABUSES OF PERCENTAGES
KEY TERMS
Absolute change=new value-reference value
Relative change (formula)
Absolute difference (formula)
Relative difference (formula)
Understand the of versus more than rule
Understand percentage points versus %
Solve percentage problems
Identify common abuses of percentages
3A: USES AND ABUSES OF PERCENTAGES
KEY IDEAS AND SKILLS
Key terms
Scientific notation
Order of magnitude
Key ideas and skills
Write and interpret numbers in scientific notation
Put numbers in perspective through
Estimation, including order of magnitude estimates
Comparisons
Scaling
3B: PUTTING NUMBERS IN PERSPECTIVE
Significant digits
Random error
Systematic error
Absolute error
Relative error
Accuracy
Precision
3C: DEALING WITH UNCERTAINTY
KEY TERMS
Distinguish significant digits from non significant zeros
Identify and distinguish between random and systematic errors
Absolute error
Relative error
Distinguish between accuracy and precision
Apply rounding rules for combining approximate numbers
Add/subtract – round to the precision of the least precise number in
the problem
Mult./division – round to the same number of significant digits as in
the number in the problem with the fewest significant digits
3C: DEALING WITH UNCERTAINTY
KEY IDEAS AND SKILLS
Key terms
Index number
Reference value
Consumer price index (CPI)
Inflation
Key ideas and skills
Understand index numbers and how they are useful for
comparisons
Understand how the CPI is used to measure inflation
Adjust prices for inflation with the CPI (formula)
3D: INDEX NUMBERS: THE CPI AND
BEYOND
Key terms
Simpson’s paradox
Test results: false +, true +, false -, true –
Key Ideas and skills
Understand and give examples of Simpson’s paradox
Understand and give examples of how mammograms and
polygraphs can lead to surprising results
Understand and give examples of how Democrats and Republicans
can make different claims about the same data even if neither side
is lying
3E: HOW NUMBERS DECEIVE: POLYGRAPHS,
MAMMOGRAMS, AND MORE
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