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Unformatted text preview: Slide 3  1 Chapter 3 Logic Slide 3  2 3.1 Statements and Logical Connectives Slide 3  3 HISTORYThe Greeks: Aristotelian logic : The ancient Greeks were the first people to look at the way humans think and draw conclusions. Aristotle (384322 B.C.) is called the father of logic. This logic has been taught and studied for more than 2000 years. Slide 3  4 Mathematicians Gottfried Wilhelm Leibniz (16461716) believed that all mathematical and scientific concepts could be derived from logic. He was the first to seriously study symbolic logic. In this type of logic, written statements use symbols and letters. George Boole (1815 1864) is said to be the founder of symbolic logic because he had such impressive work in this area. Slide 3  5 Logic and the English Language Connectives words, used to connect thoughts, such as and, or, if, then Exclusive or one or the other of the given events can happen, but not both. Inclusive or one or the other or both of the given events can happen. It is assumed in this book that or is Inclusive unless otherwise stated. Slide 3  6 Statements and Logical Connectives Statement A sentence that can be judged either true or false. Labeling a statement true or false is called assigning a truth value to the statement. Simple Statements  A sentence that conveys only one idea. Compound Statements  Sentences that combine two or more ideas and can be assigned a truth value. Slide 3  7 Quantifiers Negation of a statement  change a statement to its opposite meaning. The negation of a false statement is always a true statement. The negation of a true statement is always a false statement. Quantifiers  words such as all, none, no, some, etc Be careful when negating statements that contain quantifiers. Slide 3  8 Negation of Quantified Statements Form of statement All are. None are. Some are. Some are not. Form of negation Some are not. Some are. None are. All are. None are. Some are not. All are. Some are. Slide 3  9 Example: Write Negations Write the negation of the statement. Some candy bars contain nuts. Solution: Since some means at least one this statement is true. The negation is No candy bars contain nuts, which is a false statement. Slide 3  10 Example: Write Negations continued Write the negation of the statement. All tables are oval. Solution: This is a false statement since some tables are round, rectangular, or other shapes. The negation would be Some tables are not oval. Slide 3  11 Example of Negation of Quantifiers Write the negation of the following statements. All chicken can fly. Neg. Some chicken can not fly....
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This note was uploaded on 12/12/2011 for the course MGF 1106 taught by Professor Holbrook during the Spring '10 term at Santa Fe College.
 Spring '10
 HOLBROOK

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