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Validity of an Argument on Truth Values in Propositional Logic

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Explore the validity of a logical argument by placing truth values under premises and conclusion based on given conditions. Follow the rules to determine if the argument is valid.

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Validity of an Argument on Truth Values in Propositional Logic

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  1. Is this a VALID ARGUMENT?

  2. Place truth values under the conclusion

  3. T T false If there is a row T T F it must be one of the first two rows The conclusion is false only if p is true

  4. T T T T false Now place truth values under the second premise.

  5. F F true If there is a row T T F then it must be the second row When the conclusion is false the second premise is true only if r is false T T T T false

  6. false F In this case, we won’t find it because under these conditions the first premise is false T F F true T F T false We have eliminated all but one row in our search for the possibility T T F

  7. T F false F true T F F T false VALID There are NO conditions under which the conclusion is false when the premises are true. If the premises are true then you must accept the conclusion.

  8. Is this a VALID ARGUMENT?

  9. Place truth values under the conclusion

  10. F T T F F T false F T The conclusion is false only when r is trueand q is false

  11. F T T F F T false F T Assign values to premise #1

  12. F T T F F T false F T Assign values to premise #1

  13. T F true T T T T F F T false F T When the conclusion is false, the first premise is true only when p is true

  14. T F true T T false T T F F T F false VALID F T There are no conditions under which the conclusion is false and the premises are true.

  15. Is this a VALID ARGUMENT?

  16. Place truth values under the conclusion

  17. The conclusion is false only if r is false

  18. F F F F false F F The conclusion is false only if r is false

  19. F F F F false F F Place truth values under premise #1

  20. F F F F false F F When the conclusion is false premise #1 is true only when p is false

  21. F F true F F F F false F F F F When the conclusion is false premise #1 is true only when p is false

  22. F F true F F F F false F F F F If there is a row T T F then it is one of the yellow rows - complete them

  23. F F true F T F true F F false F F T F F If there is a row T T F then it is one of the yellow rows - complete them

  24. F F true F T F true F F false F F T invalid F F There are conditions under which the premises are true but the conclusion is false.

  25. F F The conclusion is FALSE only if r is F F false

  26. T Under these conditions, this premise is TRUE only if p is T T F true F F false

  27. T T Under these conditions, this premise is TRUE only if qT true T T F true F F false

  28. T T true F T T F true Under these conditions, this premise is TRUE only if s is F F F true F false

  29. F T T true F T Under these conditions, this premise is FALSE T F true F F true F false

  30. F T T It is not possible for all of the premises to be true when the conclusion is false. This is a valid argument. true F T false T F true F F true F false

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