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Logic Terminology

Logic Terminology. Statement- declarative sentence that is either true or false Opinion- a belief about matters commonly considered to be subjective, i.e., it is based on that which is less than absolutely certain. Law of Excluded Middle: Any statement is either true or false

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Logic Terminology

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  1. Logic Terminology

  2. Statement- declarative sentence that is either true or false • Opinion- a belief about matters commonly considered to be subjective, i.e., it is based on that which is less than absolutely certain

  3. Law of Excluded Middle: Any statement is either true or false • Law of Contradiction: A statement cannot be both true and false

  4. Deduction- when you reason from accepted statements to a conclusion or new fact, you are using deductive reasoning. • If you make an A on your Geometry test, I will give you $5.00.

  5. Suppose p is “2 + 5 = 12”. Remember a statement can be true or false. Suppose I wanted to write 2 + 5 does not equal 12. I would need the negation of p. • Suppose p is “it is sunny” • The negation of p is “it is not sunny” • Here is the way to denote negation: ~p. So any time you see ~p, what does it mean? • Negation-the denial of the statement

  6. If p is true what can we say about ∼p? • ∼p is false! • Can ∼p ever be true? • Only if p is false!

  7. Disjunctions • p: I buy you new jeans • q: I buy you new shoes • Your mom might say, “Lets go shopping. I’ll buy your new jeans OR I’ll buy you new shoes. • Disjunctions- a compound statement formed by joining two statements with the connector ‘OR’ • p v q “p or q”

  8. Conjunctions • Let’s go shopping. I’ll buy you new jeans AND I’ll buy you new shoes. • Conjunctions- a compound statement formed by joining two statements with the connector AND . • p ʌ q “p and q”

  9. http://www.youtube.com/watch?v=7udQSHWpL88

  10. Conditional Statement • Implications: if… then statement (also called the conditional statement) ‘if statement’ is the hypothesis, ‘then statement’ is the conclusion • If Johnny exercises, then he will lose weight.

  11. Symbols • ∴ -Therefore → if…., then…. • ʌ - and (intersection) • v - or ( union) • ∼ - negation

  12. Lets Practice! • What is the conclusion of the following statement? • All people who graduate high school get a job. Jessica graduates high school. • Jessica gets a job!

  13. Given p: I am an honors student. q: I play football. • ∼p I am not an honors student. 2. p ʌ ∼q I am an honors student and I do not play football. 3. ∼(p v q) ∼(I am an honors student or I play football.) I am not an honors student and I do not play football.

  14. Translate the following into symbolic logic: • 1. I do not play football. ∼ q 2. I am not an honors student and I play football. ∼ p ʌ q 3. I am an honors student or I play football. p v q

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