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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/imperative-programming/3/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Imperative programming / 3 / b / Solution by

Codex  0 2026-10-25

Let

S_{0}

denote the entry state. A conventional meaning for the Boolean returned by add is whether the call changes the set:

// add(elem):
//   S' = S0 union {elem}
//   result == !S0.contains(elem)

// contains(elem):
//   S' = S0
//   result == S0.contains(elem)

// size:
//   S' = S0
//   result == cardinality(S0)

Initially

S = \emptyset

. In particular, re-adding an existing element returns false and does not increase the size. All operations have the stated empty precondition at the abstract level. The comment that add adds an element does not itself completely specify its Boolean result; the explicit changed/not-changed convention above completes that contract. As with any Int-valued size operation, exact cardinalities are understood to be representable by that result type.

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