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# burton_discrete_logic

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### burton_discrete_logic

1. 1. Compiled By: Ni-Ni Seth Dominique Brittany Keshawn LOGIC
2. 2. Inductive and Deductive Reasoning <ul><li>Inductive reasoning- is using patterns. </li></ul><ul><li>Deductive reasoning-is using facts. </li></ul>
3. 3. <ul><li>Logical sentence that is true or false. </li></ul><ul><li>Represent statements w/ lowercase letters. </li></ul><ul><li>Simple statement- contains 1 ideal </li></ul><ul><li>Compound statement- contains several ideas. </li></ul>Statements are....
4. 4. <ul><li>Are used to join the ideas of a compound system. </li></ul><ul><li>Examples: And, Or, But, If then, and if and only if. </li></ul>Connectives
5. 5. <ul><li>Negation-express that something is not true. </li></ul><ul><li>Conjunction-idea of and. </li></ul><ul><li>Disjunction- idea of Or </li></ul><ul><li>Conditional- idea of if…then. </li></ul><ul><li>Biconditional-idea of if and only if. </li></ul>5 Connectives
6. 6. <ul><li>Universal-words such as all and every. </li></ul><ul><li>Existential-words such as some, there exsits, and there is at least one. </li></ul>Quantifiers
7. 7. <ul><li>Negation: ~ </li></ul><ul><li>Conjunction: ^ </li></ul><ul><li>Disjunction: v </li></ul>Quantifier Symbols
8. 8. <ul><li>B: The blue whale is the largest living creature. </li></ul><ul><li>~B: The blue whale is not the largest living creature. </li></ul>Negating Statements
9. 9. <ul><li>Negation- reverses the truth </li></ul><ul><li>Conjunction-both parts are true. </li></ul><ul><li>Disjunction- false when both are false. </li></ul><ul><li>Tautology- statement always true. </li></ul>Truth Tables
10. 10. Conjunction a Statement <ul><li>P: the tenant pays utilities </li></ul><ul><li>D: \$150 deposit is required </li></ul><ul><li>p^d: the tenant does not pay utilities and a \$150 deposit it is required </li></ul><ul><li>~( p^d): It is not true… </li></ul>
11. 11. Conditional and Biconditional <ul><li>Conditional-is false when T then F. </li></ul><ul><li>Biconditional-true when the components are both T or both F </li></ul>
12. 12. Conditional p  q <ul><li>Converse: If q  p </li></ul><ul><li>Inverse: ~p  ~q </li></ul><ul><li>Contrapositive: ~q  ~p </li></ul>
13. 13. <ul><li>Argument - a series of statements called Premises followed by a single statement called a conclusion. </li></ul><ul><li>An argument is valid when all premises are true. </li></ul>Verifying Arguments
14. 14. Practice Problems <ul><li>If it rains tomorrow, then I will bring an umbrella. </li></ul><ul><li>Find the Converse, Inverse, and the Contrapositive. </li></ul>
15. 15. Practice Problems Cont… <ul><li>R: the playground is wet. </li></ul><ul><li>S: the playground is cold. </li></ul><ul><li>Using the statement above make it a conjunction, disjunction, conditional, and a Biconditional. </li></ul>