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# lec0213 - Outline of COT 3100 material for first exam I...

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Unformatted text preview: Outline of COT 3100 material for first exam I. Counting A. Sum Rule B. Product Rule C. Subtraction Idea D. Permutations E. Combinations F. Combinations with repetition II. Logic A. Symbols( ∧ , ∨ , and ¬ ) B. Truth Tables C. Logic Laws D. Methods of showing equality of logical expressions E. Implication Rules F. Contrapositive of a stmt. III. Sets A. Symbols( ∩ , ∪ , ∈ , ∅ , ¬ , ∉ , and ⊂ ) B. Counting with sets C. Set Laws D. Membership Table E. Proof Techniques for if-then statements i. direct proof ii. proof of contrapositive iii. proof by contradiction F. How to Disprove an if-then statement G. Inclusion-Exclusion Principle Reading in texbook: 1.1 – 1.4, 2.1 – 2.3, 3.1 – 3.3 1) Find the number of permutations of letters of the English alphabet (i.e. strings of length 26 using each letter exactly once) that contain none of the strings math , bio or housing . Total number of permutations = 26! Permutations with math = 23! Permutations with bio = 24! Permutations with housing = 20! Permutations with both math and bio = 21! Permutations with both math and housing = 17! Permutations with both bio and housing = 0 Permutations with math, bio and housing = 0 Total = 26! – (23! + 24! + 20! – (21! + 17!) + 0) = 26! – 24! – 23! – 20! + 21! + 17! 2) In how many ways can 3 blue, 4 white and 2 red balls be distributed into 4 distinct boxes? Distributing each the blues balls is independent of distributing the white ones and the red ones. Using the technique in section 1.4 we know we can distribute 3 blues balls amongst 4 1....
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lec0213 - Outline of COT 3100 material for first exam I...

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