# SIMPSON CMSC 175 - Final Exam Study Guide (4 pages)

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# Final Exam Study Guide

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## Final Exam Study Guide

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Pages:
4
School:
Simpson College
Course:
Cmsc 175 - Discrete Mathematics

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CMSC 175 Discrete Mathematics Final Exam Study Guide The final exam is comprehensive It will include writing definitions you should know all definitions given in the lessons multiple choice questions review the multiple choice questions in the unit tests problems to solve review all problems in the homework assignments and the unit tests The final exam will not include Boolean Algebra A Logic You should know truth tables logical equivalences de Morgan s laws conditionals contrapositive converse inverse disjunctive representation negation of a conditional representation of unless and only if necessary and sufficient conditions negation of quantifies expressions arguments in propositional and predicate logic See all problems in the homework assignments and Test 1 Sample problem Show how t can be derived Premises 1 p V q 2 q r 3 p s t 4 r 5 q u s 6 Conclusion t B Proofs See all proof problems in the homework assignments and tests Sample problems Choose and apply a method of proof or disproof direct proof proof by contraposition proof by contradiction disproof by counterexample proof by mathematical induction to prove or disprove the following statements 1 For all integers n n2 is even if and only if n is even Note if and only if means a if n2 is even then n is even b if n is even then n2 is even 2 For all integers k k3 is odd if and only if k is odd 3 2 4 6 2n n n 1 for all n 1 4 12 32 52 2n 1 2 n 2n 1 2n 1 3 n 1 1 5 1 a a2 a3 a n 1 an 1 a 1 n 1 a 1 6 For all integers n if n is even then n 1 n 1 is odd 7 For all integers n if n 1 n 1 is odd then n is even 8 Consider the sequence a1 a2 an defined recursively a1 a an 1 an d Prove that an a1 n 1 d 9 The square of any integer can be written in one of the following forms 4k or 4k 1 10 Let n be an odd integer Then n3 2n2 is also odd 11 2 6 18 2 3 n 1 3n 1 n 1 12 1 2 2 3 3 4 n n 1 n n 1 n 2 3 13 32n 7 is divisible by 8 for all n 1 14 11n 6 is divisible by 5 for all n 1 15 6 7n 2 3n is divisible by 4 for all n 1 Prove A B B A

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