# Concept derivation guides

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Concept guide



## [Set membership: x∈A is a proposition, kept apart from ⊆, = and a program's membership test](/en/derivations/derivation-mko-set-membership-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-set-membership)

In a typed context let A={1,2,3}, B={1,2}, 𝓕={{1,2},{3}} (a set whose elements are sets of integers) and E={n∈ℤ ∣ 2∣n}. Decide with reasons whether each holds: 2∈A; 4∈A; B⊆A; A⊆B; B∈𝓕; {1}∈𝓕; 1000000∈E; 7∈E. Also explain why 1∈B and B∈𝓕 do not give 1∈𝓕, and why a programming language's membership test cannot replace the semantics of set membership.

Set membership

derivation-mko-set-membership-01





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