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Quantitative Reasoning Semester 1
Reasoning - logical thinking Inductive Reasoning - process of reasoning that arrives at a general conclusion based on the observation of specific examples Conjecture - educated guess Counter Example - an example that contradicts the conjecture Deductive Reasoning - process of reasoning that arrives at a conclusion based on previously accepted general statements; does not rely on specific examples Estimation - process of finding an approximate answer to a math problem Place Value - tells the value of the digit in terms of ones, tend, hundreds Bar Graph - used to compare amounts or percentages using either vertical or horizontal bars of various lengths Pie Chart/Circle Graph - constructed by drawing a circle and dividing it into parts called sectors according to the size of the percentage of each portion in relation to the whole
Line Graph/Times Series Graph - shows how the value of some variable quantity changes over a specific time period Set - collection of objects Well-Defined - for any given object, we can objectively decide whether it is or is not in the set Element/Member - each object in a set Roster Method - elements are listed between braces with commas between elements Natural Numbers - counting numbers Even Natural Numbers - even counting numbers Odd Natural Numbers - odd counting numbers Descriptive Method - uses a short statement to describe the set Set-builder Notation - uses variables, braces, and a vertical bar "|" that is read as "such that"
every element in both sets but NO repeats Difference - set of elements in set A that are not in set B; set A - set B Symbolic Logic - uses letters to represent statements and special symbols to represent words like and, or, and not Statement - Is a declarative sentence that is either true or false, but not both Paradox - something that appears to be a statement but contradicts itself Simple Statement - contains only one idea Compound Statement - Statement formed by joining two or more simple statements with a connective: and, or, if ... then, if and only if Conjunction - and Disjunction - or Conditional - if p then q; If Tessa is a chocolate lab, then Tessa is brown Biconditional -
if and only if Universal Quantifiers - all, each, every, no, none Existential Qualifiers - some, there exists, at least one Negation - opposite of truth value Truth Table - diagram in table form that is used to show when a compound statement is true or false based on the truth values of the simple statements that make up that compound statement Tautology - is a compound statement that's always true Self-Contridiction - is a compound statement that is always false Logically Equivalent - if and only if they have the same truth values for all possible combinations of truth values for the simple statements Valid - if the conclusion necessarily follows from the premises Invalid - if it's not valid Converse -
Head to Head Comparison - if a candidate wins ALL head to head comparisons then that candidate deserves to win Arrow's Impossibility Theorem - no voting method will satisfy all four of the fairness criterion
