Tessellate S.T.E.M.S - Computer Science - School - Set 3 - Problem 2

A logically omniscient machine is one which keeps on producing proofs of several propositions, such that

  1. If α \alpha is a tautology, the machine will eventually prove α \alpha .
  2. If the machine proves α \alpha and the machine proves α β \alpha \implies \beta , it will eventually prove β \beta .

Consider the following statements.

Statement I: If the machine is known to have either proven α \alpha or β \beta , then it will eventually prove α OR β \alpha \text{ OR } \beta .

Statement II: If the machine is known to have proven α OR β \alpha \text{ OR } \beta , then it will either eventually prove (or have proven) α \alpha or prove (or have proven) β \beta .

Which of them is true?


This problem is a part of Tessellate S.T.E.M.S.

Both of them Neither of them Statement II Statement I

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