Practice question · Multiple choice
Why may a line from a closed subproof not be used later in the proof?
Hints
- Ask what a line inside a subproof actually depends on.
- It holds only given the assumption, which is no longer in force once discharged.
Show the answer
B. It was derived under an assumption that has since been withdrawn
Why
Every line in a subproof is conditional on its assumption. Once discharged, that support is gone, so the line no longer stands on its own. This restriction is precisely what keeps the system sound.
Practise Natural Deduction: The Rules
The app has 3 more questions on this lesson, and keeps your place in the course. Philosophy I is free to start.
More questions on Natural Deduction: The Rules
- Arrange the steps of a conditional introduction proof in order.
- A proof of "if P then Q" by conditional introduction requires how many assumptions to be made and then…
- Which statements about natural deduction are correct?
- Truth tables establish validity by surveying every valuation, whereas natural deduction constructs a…
- Natural deduction is strictly weaker than truth tables: some valid arguments cannot be proved in it.
- Match each proof technique to the shape of reasoning it formalises.
- Sort each rule by whether it introduces or eliminates a connective.