Unformatted text preview: contrapositive, contradiction, cases. Be able to determine whether a statement is true or false, and give a proof or counterexample. Be able to prove or disprove facts about integers (even/odd), divisibility, congruence, real numbers, sets, rationality, irrationality. Be able to negate statements with quantiﬁers (possibly multiple quantiﬁers). Be able to compute in Z n . Be able to determine if a relation is an equivalence relation or a function. Be able to determine equivalence classes of an equivalence relation. Be able to tell if functions are injective, surjective, bijective. Be able to compute inverses of functions (when they exist). Be able to tell why a given function is or is not invertible. Be able to compose functions/permutations. Be able to prove theorems using induction (including theorems concerning sums, sequences, inequalities, congruences and divisibility) 1...
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 Spring '11
 Smith
 Equivalence relation, Inverse function, pg, equivalence class

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