Symbolic language — What does 'S' mean? Statements: I. '5 S # 3' means 'flowers are really good'. II. '7 # 3 5' means 'flowers are available'.

Difficulty: Medium

Correct Answer: Both Statements I and II together are not sufficient.

Explanation:


Introduction / Context:
Determine the English meaning of the symbol 'S' from two coded statements.


Given Data / Assumptions:

  • S1 tokens {5, S, #, 3} ↔ {flowers, are, really, good} (order unknown).
  • S2 tokens {7, #, 3, 5} ↔ {flowers, are, available} (four tokens for three words implies one token corresponds to a word common with S1; exact mapping still unknown).


Concept / Approach:
Use overlaps: common English words across S1 and S2 are {flowers, are}. Common tokens across sentences are {5, #, 3}. Thus, these three tokens collectively map to two words; ambiguity remains.


Step-by-Step Solution:

Since S appears only in S1, it must map to one of {really, good}. However, S1 alone cannot decide which; S2 does not include either of those words, so it cannot resolve the tie.


Verification / Alternative check:
Any attempt to force S = 'really' or S = 'good' conflicts with the bijection constraints without additional evidence.


Why Other Options Are Wrong:

  • A/B/C/E: The pair of statements does not uniquely pin 'S' to a single word.


Common Pitfalls:
Assuming token positions correspond to word order; DS problems typically treat them as sets.


Final Answer:
D — Together not sufficient.

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