Practice question · Multiple choice
A theorem's proof establishes p → q. A student concludes that q is true. What has gone wrong, and what would be needed?
Hints
- 'If it rains, the match is cancelled' is proved. Is the match cancelled?
- Ask what a conditional actually asserts about q on its own.
Show the answer
D. The implication only transfers truth if p is established
Why
A conditional promises q given p and says nothing on its own. Modus ponens needs both the implication and the premise, and forgetting the second is how a correctly proved theorem gets applied to a case it never covered, which is most of what goes wrong when a result is used outside its hypotheses.
Practise Implication and Equivalence
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