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TruthfunctionAl

TruthfunctionAl. Valid ?. John’s young or he’s wise. He’s not young. So, he’s wise. Truth-Functional Logic. John’s young or he’s wise. He’s not young. So, he’s wise. He’s wise. John is young or he is wise. He’s not young. Truth-Functional Sentence.

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TruthfunctionAl

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  1. TruthfunctionAl Valid ? John’s young or he’s wise. He’s not young. So, he’s wise.

  2. Truth-Functional Logic John’s young or he’s wise. He’s not young. So, he’s wise. He’s wise. John is young or he is wise. He’s not young.

  3. Truth-Functional Sentence Definition.* A truth-functional sentence is a compound sentence whose truth value can be determined from merely the truth values of its simplest component sentences. Example: It squawks and it flys. S & F

  4. S S & F F It squwaks. It flys. It squwaks and it flys. true false true false true true false false true false false false

  5. Example of a Truth-Functional Sentence S S & F F It squwaks. It flys. It squwaks and it flys. true false true false true true false false true false false false

  6. Which are Truth-Functional Sentences ? No a. It squawks before it flies. b. It squawks. c. It squawks because it flies. d. It does not both squawk and fly. e. It is not the case that it flies. No No Yes Yes

  7. Sentence Constant • Upper-Case Roman Letter ( C, M, R, etc.) • Stands for an actual, given sentence. • Sentence Variable • Lower-Case Roman Letter ( p, q, r, etc.) • Stands for any sentence whatever.

  8. John is young or he is wise. He’s not young. So, he’s wise. p or q not p____ q Y or W not Y____ W

  9. She’s a yak or he’s an ox. She’s not a yak.____ So, he’s an ox. p or q not p__ q Y or O not Y__ O

  10. Is Every Argument Of This FormValid ? Valid ? p or q not p_ q

  11. A Formal Truth-Functional Language • Every sentence will be either: • 1. Simple ( M, K, R, etc.) or • 2. Compound as follows : • not M • L and R • R or K Negation Conjunction Disjunction

  12. Simple sentences. Bert burped. B Wilma often laughed at the thought of Bert burping during their wedding. L

  13. Negations Bert did not burp. not B It’s not the case that Wilma often laughed at the thought of Bert burping during his speech. not W

  14. Truth-Functional Negation Negation of a sentence reverses its truth value. Roy runs. It’s not the case that Roy runs. not R R p___not p t f f t t f t f

  15. Valid Argument Forms for Negation p not not p not not p p Example not not R It’s not the case that Roy doesn’t run. R Therefore, Roy runs.

  16. Truth-Functional Conjunction Maryland remained in the Union and Virginia joined the Confederacy. M and R Form: p & q

  17. A Conjunction Claims that Both are True W R W & R Wade wades. Roy roosts. Wade wades and Roy Roosts. T F T F T T F F T F F F

  18. Valid Conjunctive Argument Forms pq p & q p & q p q p & q Not both p & q Not both p & q p q not p not q

  19. Truth-Functional Disjunction: • True when either simple sentence (“disjunct”) is true. • Claims that at least one of the disjuncts is true. Roy runs or Wade wades. p q p or q t t f t t f f f R W R or W t ttff tftf t t t t t f f

  20. Valid Disjunctive Argument Forms p or q p or q p not q not p p or q q p

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