Practice question · Multiple choice
Derived rules add no logical power to a system, yet proof construction relies on them extensively. What explains this tension, and how does it influence practical strategy?
Hints
- Does introducing a derived rule change the boundary of what can be proven?
- Why might a logician favour a concise proof over a primitive derivation?
Show the answer
B. They permit shorter proofs without altering what is derivable
Why
Derived rules are mere abbreviations for subproof patterns rather than new formal mechanics. Confusing proof brevity with system strength or structural shortcuts overlooks that every valid step remains strictly reducible to primitive natural deduction rules.
Practise Proof Strategy
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More questions on Proof Strategy
- Modus tollens, hypothetical syllogism, disjunctive syllogism and contraposition are all derived rules. How…
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