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Quantitative Reasoning (Chapter 1 & 2) complete questions and answers
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 - 1. 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 F T (If p is true (T), not p is false (F)) (If p is false (F), not p is true (T)) Double Negation - Not not p, has the same truth value as p P NOT P NOT NOT P
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 - Two sets that have members in multiple categories Categorical Propositions - Must have the structure of a complete sentence. One set appears in the subject, the other appears in the predicate. For example, "All whales are mammals", the set whales is the subject set, while the set mammals is the predicate set. Use the letter "S" to represent subject and "P" to represent predicate, so we can rewrite "all whales are mammals" as "all S are P", where S = Whales and P = Mammals Inductive - Specific premises to a general conclusion. Does not prove its conclusion true, so it is evaluated based on its strength.
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 - 1. 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
