Lecture3.1 - IS2150/TEL2810 JamesJoshi...

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1 IS 2150 / TEL 2810 Introduction to Security James Joshi Associate Professor, SIS Lecture 3.1 September 13, 2011 Mathematical Review Security Policies
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Objective Review some mathematical concepts Propositional logic Predicate logic Mathematical induction Lattice 2
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3 Propositional logic/calculus Atomic, declarative statements (propositions)  that can be shown to be either TRUE or FALSE but not  both; E.g., “Sky is blue”; “3 is less than 4” Propositions can be composed into compound  sentences using connectives Negation  ¬   p    ( NOT ) highest precedence Disjunction    q ( OR second precedence Conjunction    q ( AND ) second precedence Implication  q  q logical consequence of p  Exercise: Truth tables?
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4 Propositional logic/calculus Contradiction:  Formula that is always false : p    ¬ p What about:  ¬ (p    ¬ p)? Tautology:  Formula that is always True : p    ¬ p What about:  ¬ (p    ¬ p)? Others Exclusive OR:  p   q; p or q but not both Bi-condition: p   q    [p  if and only if  q (p iff q)] Logical equivalence: p   q [p is logically equivalent to q] Some exercises…
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5 Some Laws of Logic Double negation DeMorgan’s law ¬ (p 
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Lecture3.1 - IS2150/TEL2810 JamesJoshi...

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