In a code language, how is the word ‘‘cost’’ written? I. The phrase ‘‘cost was very high’’ is coded as ‘‘& 6 # 1’’. II. The phrases ‘‘some cost was discount’’ and ‘‘some people like discount’’ are coded as ‘‘1 8 7 #’’ and ‘‘8 7 5 %’’ respectively. (Assume a consistent one-word↔one-code mapping.)

Introduction / Context:
We must identify the exact code for ‘‘cost.’’

Given Data / Assumptions:

• I: {cost, was, very, high} → {&, 6, #, 1} (order unknown).
• II: ‘‘some cost was discount’’ → {1, 8, 7, #}; ‘‘some people like discount’’ → {8, 7, 5, %}.
• Consistent one-to-one word↔code mapping is assumed.

Concept / Approach:
Use intersections of code sets from sentences sharing common words to isolate candidates.

Step-by-Step Reasoning:
From II: Common words between the two sentences are ‘‘some’’ and ‘‘discount’’ ⇒ common codes are {8, 7}. Thus in the first sentence of II, the remaining codes {1, #} must correspond to {cost, was} (order unknown).From I: {cost, was, very, high} → {&, 6, #, 1}. This is consistent with {cost, was} being {#, 1}, but still does not distinguish which of # or 1 maps to ‘‘cost’’.Even using both statements, ‘‘cost’’ ∈ {#, 1} and remains ambiguous.

Why Other Options Are Wrong:
Neither I nor II alone isolates a single code; combining still leaves two possibilities. Hence “both necessary” is insufficient and incorrect; only “neither…nor both together” fits.

Final Answer:
Neither statement alone nor both together are sufficient.