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COT3100FinalExamReview - COT 3100 Topics Covered Logic Use...

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COT 3100 Topics Covered Logic : Use of truth tables, logical connectives, implications, logic and implication laws, use of quantifiers Sets : Definition, Union, Intersection, Minus, Some Counting, Set Laws, Set Table, Venn Diagrams, Inclusion/Exclusion Principle Counting: Sum Principle, Product Principle, Subtraction Principle, Permutations, Combinations, Combinations with repetition Relations & Functions: Definition of a relation, reflexive, irreflexive, symmetric, anti-symmetric, transitive, injection, surjection, and bijection Number Theory: Induction, Definition of divisibility, Use of mod and mod rules, Euclid’s Algorithm, Extended Euclidean Algorithm, Fundamental Theorem of Algebra, Proof that 2 is irrational. Relevant parts in the book: Counting: 1.1 - 1.4 Logic 2.1 – 2.4 Sets 3.1- 3.3 Number Theory 4.1 – 4.5 Relations & Functions 5.1,5.2,5.6,7.1,7.3,7.4 Since we have not had an exam with functions and relations, that will be the stress of the exam. No need to memorize the logic or set laws – I will attach the necessary tables.
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Logic problem Show that the following is a tautology: ( (p r) ( (q r) p) ) ¬ ( ( ¬ (p q) ) p ). ( (p r) ( (q r) p) ) ¬ ( ( ¬ (p q) ) p ) ( (p r) ( (q r) p) ) ¬¬ ( p q) ¬ p (De Morgans) ( (p r) ( (q r) p) ) ( p q) ¬ p (Double Negation) ( ¬ p p) ( (p r) (q r) (p q)) (Com/Assoc. over or) T ( (p r) (q r) (p q)) (Inverse Law) T (Domination Law) Set Problem Prove or disprove: ((A C) (B C)) ((A B) – C = ) PROVE if ((A C) (B C)), that means we can assume if x A, then x C, and if x B then x C. Now, we need to show that ((A B) – C = ).
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