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,, + " -". + a,, Meaning SectionFormal Logic"--p Not p p and q p or q q p implies q q p is equivalent to q X S logically implies X 3 AKP Conjecture about complexity (Vx)P(x) For all x, P(x) (3x)P(x) There exists an x such that P(x) (VxE V)P(x) For all X EV, P(x) (3x E V)P(x) There exists an x E V such that P(x) [i.]

1.12.4 Using Discrete Mathematics in Computer Science 87 CHAPTER 2 Formal Logic 89 2.1 Introduction to Propositional Logic 89 2.1.1 Formulas 92 2.1.2 Expression Trees for Formulas 94 2.1.3 Abbreviated Notation for Formulas 97 2.1.4 Using Gates to Represent Formulas 98 2.2 Exercises 99 2.3 Truth and Logical Truth 102

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