1. Mr. Cervone

2. History of Logic - Aristotle Aristotle Greek philosopher 384 BC – 322 BC Born in Stageira, Chalcidice (Thessaloniki – Greece) Studied at Plato’s Academy of Athens since he was 18 Father of logic Believed that logic should be build out of syllogism

3. History of Logic - Syllogism Syllogism: Starting from true statements followed by statements that must be true as well I.e. “If all monkeys are primates, and all primates are mammals, then all monkeys are mammals”. Learn new knowledge based on old knowledge

4. History of Logic – George Boole George Boole English mathematician & phylosopher 11/2/1815 – 12/8/1864 Inventor of Boolean Logic Gave rise to computer science

5. History of Logic – Boolean Logic Boolean Logic Truth values 0 and 1 Conjunction Disjunction Negation

6. Logic & Geometry What is Geometry? Branch of mathematics that defines and relates the basic properties and measurement of line segments and angles I.e. All angles in a triangle add up to 180°, etc. What does Logic have to do with Geometry? investigate how these geometric properties interact to form a logical system logical system must start with generally accepted terms and concepts that are building blocks of the system.

7. Logic & Geometry Truth: Begin somewhere with truths that are accepted without argument  Axioms I.e. Point is that which has no part I.e. Line is breathless length I.e. Set as a collection of objects I.e. Plane as a set of points forming a surface

8. What is Logic Examples SentenceType The Brooklyn Bridge is in New YorkTrue mathematical sentence (T) The capital of California is Los AngelesFalse mathematical sentence (F) Did you have soccer practice today?Nonmathemtical sentence 19-2Nonmathemtical sentence 5x = 10Open sentence: the variable is x Jenny found it behind the sofaOpen sentence: the variable is it

9. Negation Examples The negation of a statement always has the opposite truth value of the given or original statement and is usually formed by adding the word not to the given statement.