Unformatted text preview: contrapositive, contradiction, cases. Be able to determine whether a statement is true or false, and give a proof or counterex-ample. Be able to prove or disprove facts about integers (even/odd), divisibility, congruence, real numbers, sets, rationality, irrationality. Be able to negate statements with quanti-ﬁers (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, sur-jective, 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
- Equivalence relation, Inverse function, pg, equivalence class