Practice question · Select all that apply
Which statements about natural deduction are correct?
Hints
- Three describe the system; one would make it unsound.
- Natural deduction and truth tables agree exactly, that is soundness and completeness.
Show the answer
- B. Assumptions must be discharged before a proof is complete
- C. Conditional elimination is modus ponens
- D. Each connective has an introduction and an elimination rule
Why
The system is sound (everything provable is valid) and complete (everything valid is provable), so it can never disagree with the tables. Both properties had to be proved and neither is obvious.
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.
- Why may a line from a closed subproof not be used later in the proof?
- A proof of "if P then Q" by conditional introduction requires how many assumptions to be made and then…
- 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.