# Concept derivation guides

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

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Concept guide



## [Subset: proving inclusion from an arbitrary element and refuting it by a counterexample](/en/derivations/derivation-mko-subset-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-subset)

In the universe ℤ, let A be the set of multiples of 6, B the set of even integers and C the set of multiples of 4. Prove A⊆B and that this inclusion is strict (A≠B); prove A⊄C even though A and C share the element 12; note that B⊆B holds (⊆ allows equality); and prove {6}⊆A ⇔ 6∈A while separating the type roles of the two statements.

Subset

derivation-mko-subset-01



Concept guide



## [The complete reachable-subset DFA of an epsilon-NFA](/en/derivations/derivation-mko-subset-construction-nfa-to-dfa-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-subset)

List every transition and prove language equivalence by prefix induction.

Subset construction from an NFA to a DFA

derivation-mko-subset-construction-nfa-to-dfa-01





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