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# Intro to logic

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### Intro to logic

1. 1. Introduction to Logic * Please copy all notes in white font
2. 2. Statements <ul><li>Symbolic Logic uses symbols to represent statements </li></ul><ul><ul><li>Statement- A declarative sentence that is either true or false </li></ul></ul><ul><ul><li>Examples; </li></ul></ul><ul><ul><ul><ul><li>Some cows have spots </li></ul></ul></ul></ul><ul><ul><ul><ul><li>P-3 3 = 17 </li></ul></ul></ul></ul>
3. 3. Statements <ul><li>Non- examples </li></ul><ul><ul><li>Poo smells bad </li></ul></ul><ul><ul><li>Is the weather is warm? </li></ul></ul><ul><ul><li>This sentence is false </li></ul></ul><ul><ul><li>Write your notes! </li></ul></ul><ul><ul><ul><li>Why are they not statements? </li></ul></ul></ul><ul><ul><ul><li>They are not “true” or “false” </li></ul></ul></ul><ul><ul><li>An opinion </li></ul></ul><ul><ul><li>A question </li></ul></ul><ul><ul><li>A paradox </li></ul></ul><ul><ul><li>A command </li></ul></ul>
4. 4. Compound Statements <ul><li>Formed by two or more statements </li></ul><ul><li>Logical connectives (aka connectives) </li></ul><ul><ul><ul><ul><li>AND </li></ul></ul></ul></ul><ul><ul><ul><ul><li>OR </li></ul></ul></ul></ul><ul><ul><ul><ul><li>NOT </li></ul></ul></ul></ul><ul><ul><ul><ul><li>IF….THEN </li></ul></ul></ul></ul>
5. 5. Compound Statements <ul><li>Are these compound statements? </li></ul><ul><ul><ul><li>I am older than you, and I am better at math </li></ul></ul></ul><ul><ul><ul><li>You can run, or you can hide </li></ul></ul></ul><ul><ul><ul><li>His T-shirt is made by Abercrombie and Fitch </li></ul></ul></ul><ul><ul><ul><li>If she says so, then it must be true </li></ul></ul></ul><ul><ul><ul><ul><li>Yes- notice the logical connective “and” </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Yes- “or” </li></ul></ul></ul></ul><ul><ul><ul><ul><li>No – “and” is not a logical connective statement </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Yes – “If…then” </li></ul></ul></ul></ul>
6. 6. Forming Negations
7. 7. <ul><li>The opposite or “not” statement </li></ul><ul><li>The negation of a true statement is false AND </li></ul><ul><li>The negation of a false statement is true </li></ul>Negation
8. 8. <ul><li>President Bush was an idiot </li></ul><ul><li>Vincent is a human being </li></ul><ul><li>Introduce a “not” to the statement </li></ul><ul><li>President bush was not an idiot </li></ul><ul><li>Vincent is not a human being </li></ul>Write the Negation of; Examples
9. 9. A negation must have the Opposite truth value as the other statement Negation
10. 10. Review; Inequality Symbols
11. 11. A negation must have the Opposite truth value as the other statement Give the negation of each statement, but don’t use a slash symbol
12. 12. More symbols <ul><li>Example; use the connective ~ </li></ul><ul><li>If p represents the statement “George Bush was a competent President”, then </li></ul><ul><li>~p represents; </li></ul><ul><ul><li>“ George Bush was not a competent president” </li></ul></ul>
13. 13. Examples
14. 14. Quantifiers <ul><li>Universal Quantifiers </li></ul><ul><ul><li>All </li></ul></ul><ul><ul><li>Each </li></ul></ul><ul><ul><li>Every </li></ul></ul><ul><ul><li>No/ None </li></ul></ul><ul><li>Existential Quantifiers </li></ul><ul><ul><li>Some </li></ul></ul><ul><ul><li>Here exists </li></ul></ul><ul><ul><li>(for) at least one </li></ul></ul>Quantifiers are used in mathematics to indicate how many of a particular situation exist