1. Predicate Calculus

# 1. Predicate Calculus - MATH 224 Discrete Mathematics...

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1 08/27/09 MATH 224 – Discrete Mathematics Predicate Calculus Some of the statements that are important in mathematics and computer science are not propositions. For example, X % 2 == 0 is not true for all integers, but only even integers. In order to make statements about the truth of this type of statement it is necessary to introduce the quantifiers for all and there exists . So for example, we can make a statement about an array of integers such as the upper bound below. all A i an element of A. That of course is a true statement.

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2 08/27/09 MATH 224 – Discrete Mathematics Predicate Calculus Predicate calculus allows us to make precise statements about the properties of a specific data structure. Consider the example below.
3 08/27/09 MATH 224 – Discrete Mathematics Predicate Calculus Predicate calculus allows us to make precise statements about the properties of a specific data structure. Consider the example below.

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4 08/27/09 MATH 224 – Discrete Mathematics Predicate Calculus What are some values for n 0 and c that will make the predicate clause above true?
5 08/27/09 MATH 224 – Discrete Mathematics Substitution of Quantifiers What are the equivalent predicates for the following with replaced by and replaced by .

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6 08/27/09 MATH 224 – Discrete Mathematics Order of Quantifiers
7 08/27/09 MATH 224 – Discrete Mathematics Order of Quantifiers

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8 08/27/09 MATH 224 – Discrete Mathematics Proofs In the predicate calculus it is not possible to use truth tables to prove most results since statements depend on one or more variables. This makes the job of proving results quite a bit more difficult. Logical systems consists of a set of definitions, axioms, and rules of inference.
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## This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Spring '08 term at Southern Illinois University Edwardsville.

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1. Predicate Calculus - MATH 224 Discrete Mathematics...

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