Practice question · Put in order
Arrange the steps of a conditional introduction proof in order.
- Reach the consequent inside the subproof
- Assume the antecedent as a temporary supposition
- Conclude the conditional outside the subproof
- Discharge the assumption
- Derive intermediate results within the subproof
Hints
- The assumption comes first and is withdrawn last.
- The conditional itself can only be asserted once the assumption has been discharged.
Show the answer
- Assume the antecedent as a temporary supposition
- Derive intermediate results within the subproof
- Reach the consequent inside the subproof
- Discharge the assumption
- Conclude the conditional outside the subproof
Why
To prove "if P then Q", suppose P and reach Q. The conditional is asserted only after discharge, and it no longer depends on the assumption, which is exactly what makes it a categorical result.
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
- 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…
- 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.