VALID AND SOUND ARGUMENTS: TEN ORIGINAL EXAMPLES
QUESTIONS ONLY

For each original fictional case, write (1) whether the form is valid and why; (2) which premises are true, false or unverified in the supplied record; and (3) whether soundness is established. For an invalid form, supply a situation with every premise true and the conclusion false. A false premise is not a counterexample to validity. Use classical propositional logic, the material conditional and inclusive or. Unknown evidence does not make a claim false. Records are only for the truth check; do not add them as premises.

Material conditional: if p then q is false only when p is true and q false. Inclusive or allows both alternatives.

Case 1: Fictional dispatch record A: parcel N is sealed and scanned. P1: If N is sealed, N is scanned. P2: N is sealed. C: N is scanned. Treat this record as the complete supplied evidence about these two properties. Is the argument valid? Is it sound in this scenario?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 2: Fictional dispatch record B: parcel N is sealed but not scanned. Use exactly the same argument: P1: If N is sealed, N is scanned. P2: N is sealed. C: N is scanned. What changed from case 1: the inference form, the truth of a premise, or both?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 3: Fictional dispatch record C: parcel N is not sealed, but it is scanned. Again, P1: If N is sealed, N is scanned. P2: N is sealed. C: N is scanned. Evaluate this classroom conditional using the truth-table convention explained below. Does the true conclusion make the argument sound?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 4: Return to record A: N is sealed and scanned. P1: If N is sealed, N is scanned. P2: N is scanned. C: N is sealed. All three statements match this record. Is this enough to establish validity and soundness?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 5: Use record C: N is not sealed but is scanned. P1: If N is sealed, N is scanned. P2: N is not sealed. C: N is not scanned. Test the inference first, then compare each statement with the supplied record.
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 6: Fictional dispatch record D: N is neither sealed nor scanned. P1: If N is sealed, N is scanned. P2: N is not scanned. C: N is not sealed. Compare this argument with case 5: which part of the conditional is denied?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 7: A fictional notification record says that notice J was printed and was not emailed. P1: J was emailed or printed, or both. P2: J was not emailed. C: J was printed. Is the explicitly inclusive “or” a problem for this inference?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 8: A different fictional record says notice K was emailed and not printed. P1: K was emailed or printed, or both. P2: K was emailed. C: K was not printed. C is true in this record. Does it follow from P1 and P2?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 9: A fictional archive note asserts P1: report Z has been checked and filed. C: Report Z has been checked. No check log or filing record is supplied, and you cannot determine whether P1 is true. Assess the inference, then state precisely what the missing evidence prevents you from concluding.
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______

Case 10: A fictional three-event record says a parcel was not checked, was filed and received a receipt. P1: If it was checked, it was filed. P2: If it was filed, it received a receipt. C: If it was checked, it received a receipt. Evaluate the two conditionals using the same classroom convention. Does the conclusion assert that checking actually occurred?
Validity and reason: ______
Premise truth: ______
Soundness and evidence: ______
Counterexample, if invalid: ______