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Discrete Mathematics Homework Help | Software Engineering Mathematics

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Introduction And Propositions

In this tutorial, we will study the heart of discrete mathematics:

  • propositional logic: making statements

  • set theory: describing collections of objects

  • predicate logic: making statements about objects

  • relations, functions, sequences: describing relationships between objects

  • recursion and induction: reasoning about repeated application (and returning definitions

If you need any help related to software engineering mathematics(Discrete Mathematics) then contact us or send your requirement details so we can help you.


Contents

  • Discrete mathematics

  • The Z notation

  • Propositions

  • Tautologies

  • Equivalences


The Z notation

The syntax and semantics that we choose for discrete mathematics is that of the Z notation:

  • The logic is typed: every identifier in our mathematical document is associated with a unique basic set

  • Functions are partial by default: the result of applying a function to a particular object may be undefined

  • The various sub-languages are precisely defined: a Z document is easily parsed and type-checked

Propositions

A proposition is a statement that must be either true or false Note that we deal with a two-valued logic (cf. SQL) Propositions may be combined using logical connectives The meaning of a combination is determined by the meanings of the propositions involved.


Examples

  • 2 is even

  • 2 + 2 = 5

  • tomorrow = tuesday

  • she is rich

  • he is tall

  • 2 / 0 = 0

Examples

  • ¬ (2 is an even number)

  • she is rich ∧ he is tall

  • the map is wrong ∨ you are a poor navigator

  • (2 + 2 = 5) ⇒ (unemployment < 2 million)

  • (tomorrow = tuesday) ⇔ (today = monday)


Truth Table

We use truth tables to give a precise meaning to our logical connective

Practice Example:











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