Modesto Junior College



Math 101 – Exam 2 ReviewHistorical Figures John VennAristotleGottfried LeibnitzGeorge BooleCharles Dodson (what is his pseudonym?)Math Concepts (MW) Hamilton Circuits – number of possible circuits (by brute force), approximating a circuit using the cheapest link and nearest neighbor algorithmsDeductive vs. inductive reasoning (and examples that fall under each category)Pattern recognition to deduce new examplesVenn Diagram construction - Representing “all”, “some” and “no”, and also representing NOT, AND, IF, and IMPLIESSyllogisms and determining validityStatementsCompound statements and their operators: not, and, or, conditional Translating English statement to symbols and symbols to English statementsNecessary and sufficient conditions – writing in symbolic logic, rewriting in “if p then q” formatVariations on conditionals – converse, inverse, and contrapositive“If” vs. “Only If” – finding the premise & conclusion, writing in symbolic logic, rewriting in if p then q format.Tautology and contradictionUsing truth tables to:represent statements containing operators (not, and, or, conditional)determine whether expressions are equivalentuse DeMorgan’s law to find the negation of a compound statementrepresent “if”, “only if” and “If and only if” conditionalsAnalyze arguments to determine whether the given hypotheses leading to a conclusion provide a valid argumentDetermine the circumstances which make an argument invalidSets and their propertiesWell-defined setsRoster vs. set-builder notationCardinal numbersEmpty setsThe Universal setProper and improper subsetsUnion and Intersectionthe Cardinal Number formula (related to union and intersection)Mutually exclusive setsThe Complement of a SetVenn Diagram Shading for applicationsApplicationsFields of study where logic is usedCalculator digits – How can you combine 7 small LED’s to make the digits 0 through 9 using logic?Video games – Example of how conditionals/outcomes are used in the creation of gamesCardinal numbers – Given the number of people/objects in categories, find the number of people/objects in related categoriesSample Logic ProblemsA) All musicians are artistsB) No musicians are richa) Represent the statements A and B using a Venn diagram:b) Is it true that no artists are rich?c) Is being a musician necessary, sufficient, or neither for being an artist?p: He is an elephant.q: He is old.r: He forgets.a) Translate to symbolic logic: “He is an elephant or he does not forget”b) Write the negation of the symbolic representation in part “a)” above, using DeMorgan’s law to simplify.c) Write the statement of part “b)” in words.d) Translate to symbolic logic: “If he is an elephant and is not old, he does not forget.”For the statement, “If it’s not raining, I’ll go to the park.”a) Translate to the statement to symbolic logic, writing your own statements for p and q.b) Write the converse of the original statement in words.c) Write the inverse of the original statement in words.d) Write the contrapositive of the original statement in words.a) Use truth tables to represent the statements:Statement 1: ~(p q) Statement 2: p ^ ~qb) Are these statements equivalent? Why or why not? Consider the statements: p: I’m sickq: I take medicinea) Write symbolic logic for the hypotheses and conclusion of the argument below:Hyp. 1) If I’m sick, I take medicine.____________________________________Hyp. 2) I’m not sick or I take medicine.____________________________________Therefore, I don’t take medicine. _____________________________________b) Construct a truth table and state whether the argument is valid. If not, state conditions for which it is invalid. ................
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