3.5 Symbolic Arguments 151 Exercises Warm Up Exercises In Exercises 1– 6, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. When the conclusion of an argument necessarily follows from the given set of premises it is a(n) ________ argument. Valid 2. When the conclusion of an argument does not necessarily follow from the given set of premises it is a(n) ________ argument. Invalid 3. An argument that is invalid is also known as a(n) ________. Fallacy 4. To determine the validity of an argument with two premises, construct a truth table of the form [(premise 1) ∧ (premise 2)] → ________. Conclusion 5. If the conditional statement referred to in Exercise 4 is a tautology, then the argument is a(n) ________ argument. Valid 6. If the conditional statement referred to in Exercise 4 is not a tautology, then the argument is a(n) ________ argument. Invalid Practice the Skills For Exercises 7–12, fill in the blank to identify the standard form of the argument. 7. p q p q ~ ∨ ∴ Disjunctive ________. Syllogism 8. p q p q → ∴ Law of ________. Detachment 9. p q p q ~ ~ → ∴ Fallacy of the ________. Inverse 10. p q q p → ∴ Fallacy of the ________. Converse 11. p q q r p r → → ∴ → Law of ________. Syllogism 12. p q q p ~ ~ → ∴ Law of ________. Contraposition In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. 13. a b a b ~ ~ → ∴ Invalid 14. a b a b ~ ∨ ∴ Valid 15. e f e f → ∴ Valid 16. g h h i g i → → ∴ → Valid 17. j k k j ~ ∨ ∴ Valid 18. l m m l ~ ~ → ∴ Valid 19. n o o n → ∴ Invalid 20. r s r s → ∴ Valid 21. t u u t ~ → ∴∼ Valid 22. v w w v → ∴ Invalid 23. x y y z x z → → ∴ → Valid 24. x y x y ~ ~ → ∴ Invalid 25. p q q r p r ↔ ∧ ∴ ∨ Valid 26. p q q r r p ~ ~ ↔ → ∴ → Valid 27. p r p q p r ~ ↔ ∧ ∴ ∧ Invalid 28. p q p r q ∨ ∧ ∴ Invalid 29. p q q r r p p → ∨ ∨ ∴ Invalid 30. p q q r r p p r → → → ∴ ↔ Valid 31. p q r p p r q p ~ ~ → → ∨ ∴ ∨ Valid 32. p q q r r p p r ~ ~ ~ ∨ ∨ ∨ ∴ ∨ Invalid SECTION 3.5
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