# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Counterexamples and domain eligibility: primality of n²+n+11, the failure set and the least counterexample](/en/derivations/derivation-mko-counterexample-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-counterexample)

Let U={n∈ℤ ∣ 0≤n≤12}, V={n∈ℤ ∣ 0≤n≤9}, m(n)=n²+n+11 and P(n): 'm(n) is prime'. Decide φ_U: ∀n∈U P(n); find the failure set F_U and the least counterexample; decide whether the candidate −11 is eligible; and decide φ_V: ∀n∈V P(n).

Counterexamples and domain eligibility

derivation-mko-counterexample-01





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