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Discrete Mathematics for Computer Science - UH

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,, + " -".

Functions 219 4.1 Basic Definitions 219 4.1.1 Functions as Rules 221 4.1.2 Functions as Sets 222 4.1.3 Recursively Defined Functions 224 4.1.4 Graphs of Functions 225 4.1.5 Equality of Functions 226 4.1.6 Restrictions of Functions 228 4.1.7 Partial Functions 229 4.1.8 1-1 and Onto Functions 231

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