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Quantitative Reasoning (Chapter 1 & 2)
Logic - The study of methods and principles of reasoning Argument - Uses a set of facts or assumptions, called premises, to support a conclusion Fallacy - A deceptive argument -- an argument in which the conclusion is not well supported by the premises Appeal to Popularity - Many people believe p is true; Therefore.... p is true False Cause - A came before B; Therefore... A caused B Appeal to Ignorance - There is no proof that p is true; Therefore... p is false Hasty Generalization - A and B are linked one or a few times; Therefore... A causes B (or vice versa) Limited Choice - p is false; Therefore... only q can be true Appeal to Emotion - p is associated with a positive emotional response; Therefore... p is true Personal Attack -
I have a problem with the person or group claiming p; Therefore... p is not true Circular Reasoning - P is true. P is restated in different words. (The argument states the conclusion) Diversion (Red Herring) - P is related to q and I have an argument concerning q; Therefore... p is true Straw Man - I have an argument concerning a distorted version of p; Therefore... I hope you are fooled into concluding I have an argument concerning the real version of p 5 Steps for Evaluating Media Source -
- Consider Source
- Check the Date
- Validate Accuracy
- Watch for Hidden Agendas
- Don't Miss the Big Picture Proposition - Makes a claim (either an assertion or a denial) that may be either true or false. I must have the structure of a complete sentence Truth Table - A table with a row for each possible set of truth values for the propositions being considered Negation - A proposition that makes the opposite claim of a proposition "p" P NOT P T F
Disjunction - Given two propositions, p and q, the statement p or q is called their.... It is true unless p and q are both false P Q P OR Q T T T T F T F T T F F F Conditional Proposition (Implication) - A statement in the form of if p, then q is called... It is true unless p is true and q is false Hypothesis. Conclusion. P. Q. If P Then Q T. T. T T. F. F F. T. T F. F. T Proposition P = Hypothesis Proposition Q = Conclusion Conditional - If it is raining, the I will bring an umbrella to work (If p, then q) Converse - If I bring an umbrella to work, then it must be raining (if q, then p)
Inverse - If it is not raining, I will not Brin gnat umbrella to work (If not p, then not q) Contrapositive - If I do not bring an umbrella to work, then it must not be raining (If not q, then not p) Logically Equivalent - Two statements that share the same truth values Converse and Inverse Conditional and Contrapositive Set - Collection of objects Members - of a set, the individual objects within it Written by listing within a pair of braces, {} Use three dots ... to indicate a continuing pattern if there are too many members to list Venn Diagram - A diagram that uses circles to represent sets Subset - A set inside of a set Disjoint - Sets that have nothing in common Overlapping -
Divison Example: Read miles / hours as "miles per hour" Of or Hyphen (-) - Multiplication Example: Read Kilowatts x hours as "kilowatt-hours" Square - Raising to the second power Example: Read ft x ft, or ft^2, as "square feet" or "feet squared" Cube or Cubic - Raising to the third power Example: Read ft x ft x ft, or ft^3, as "cubic feet" or "feet cubed" Conversion Factor - A statement of equality that is used to convert between units Four Step Problem-Solving Process -
- Understand the Problem
- Devise a Strategy for Solving the Problem
- Carry Out Your Strategy, and Revise if Necessary
- Look Back to Check, Interpret, and Explain Your Result
