MA112-Lecture_Notes-OH-L01

MA112-Lecture_Notes-OH-L01 - MA112 Discrete Mathematics...

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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 1 MA112 Discrete Mathematics Omar Hamdy omar.hamdy@gmail.com Lecture Notes 1
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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 2 Discrete Mathematics • Discrete mathematics is the study of objects or structures that are distinct or discrete rather than continuous. • Study of discrete mathematics is the essence of computer science studies.
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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 3 Logic • Logic is a mean to represent knowledge and logical inferences. • Logic defines: – Syntax of statements – The meaning of statements – The rules of logical inference • Propositional Logic is the simplest logic and the core of this course.
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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 4 Propositional Logic • A statement is a description of something – An apple is a fruit – The oceans are made of fresh water – What are the possible outcomes? – Axiom: False is the opposite of truth – What is the opposite of y > 5? • A proposition is a declarative statement that is true or false.
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MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 5 Propositional Logic • Which are popositions – The year is 266 days – 2 + 2 = 4 – How are you? – Help me out – He is smart – X + 1 < 4 – It will rain today
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Dr. Omar Hamdy Summer 2010 6 Propositional Logic • Propositional Logic is a static discipline of statements which lack semantic content: – p = An apple is a fruit – q = The list of fruits includes apples – r = The sun is larger than the moon – In propositional calculus, all the above are equally related because they are all true. Semantically, p and q are the same thing.
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MA112-Lecture_Notes-OH-L01 - MA112 Discrete Mathematics...

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