Transcription of Discrete Mathematics for Computer Science
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Discrete Mathematics for Computer Science
I. = . 1. ! |~ilHTerms Meaning SectionSets, Proof Templates, and Inductionx e A x is an element ofA f A x is not an element ofA x E A and P(x)} Set notation Natural numbers Integers Rationals Real numbers = B Sets A and B are equal C B A is a subset of B g B A is nota subset of B C B A is a proper subset of B 5 B A is nota proper subset of B a bimplies a b a if and only if b A union B A intersect B Generalized union of family of sets X Generalized intersection of family of sets X Xi Xm U ..UXn Xm n .. n Xn -B Elements of A not in B Elements not in A D B (A U B) -(A n B) (X) Power set of X x Y Product of X and Y A y Meet ofx and y v y Join ofx and y Complement of x Top Bottom Cardinality of A a,, + " -".
2.5.2 Application: DNF and Combinatorial Networks 124 2.5.3 Conjunctive Normal Form 125 2.5.4 Application: CNF and Combinatorial Networks 127 2.5.5 Testing Satisfiability and Validity 127 2.5.6 The Famous 'P Af r Conjecture 129 2.5.7 Resolution Proofs: Automating Logic 129 2.6 Exercises 131 2.7 Predicates and Quantification 134
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