In a certain code language, the sentences "book is tough", "tough can easy" and "easy not book" are written as "fu la mi", "fu muk po" and "ti po la" respectively. What is the code for the word "tough" in that language?

Introduction / Context:
This coding decoding question uses a word code language where each English word is represented by a unique code word. You are given three coded sentences and must determine which code corresponds to the word "tough". This kind of problem tests logical deduction by comparing overlapping information from multiple coded statements.

Given Data / Assumptions:
- "book is tough" is written as "fu la mi".
- "tough can easy" is written as "fu muk po".
- "easy not book" is written as "ti po la".
- Each English word has a unique code word, and vice versa.
- The order of words and codes is not necessarily the same, only the set membership matters.

Concept / Approach:
The method is to use set intersections of code words for sentences that share common English words. If two sentences contain the same English word, then their code sets must share a common code word. By comparing different pairs of sentences, we can map out which code stands for "book", which for "tough", and which for "easy". Once the mapping is clear, answering the question is straightforward.

Step-by-Step Solution:
Step 1: From "book is tough" → "fu la mi", we know that the words book, is, tough correspond to the code set {fu, la, mi}. Step 2: From "tough can easy" → "fu muk po", the words tough, can, easy correspond to {fu, muk, po}. Step 3: From "easy not book" → "ti po la", the words easy, not, book correspond to {ti, po, la}. Step 4: Consider the word "book", which appears in the first and third sentences. The common code between {fu, la, mi} and {ti, po, la} is "la", so "book" corresponds to "la". Step 5: Consider the word "easy", which appears in the second and third sentences. The common code between {fu, muk, po} and {ti, po, la} is "po", so "easy" corresponds to "po". Step 6: Now in the first and second sentences, the common English word left in both is "tough". The common code between {fu, la, mi} and {fu, muk, po} is "fu". Therefore, "tough" corresponds to "fu".

Verification / Alternative check:
With the mapping book → la, easy → po, tough → fu, we can verify the sentences. For "book is tough", the code set {fu, la, mi} must include la and fu for book and tough, which it does. For "tough can easy", the code set {fu, muk, po} includes fu for tough and po for easy. Finally, "easy not book" has {ti, po, la}, containing po for easy and la for book. All are consistent, confirming the mapping.

Why Other Options Are Wrong:
- Option mi is unused in the overlaps and does not uniquely correspond to "tough".
- Option po has been shown to represent "easy", not "tough".
- Option la has been determined to represent "book".

Common Pitfalls:
A common mistake is to assume a one to one mapping without checking all overlapping sentences, leading to incorrect associations. Another is to rely on the order of words instead of treating codes and words as unordered sets. Always use intersections of code sets for sentences sharing the same English word and confirm consistency across all sentences.

Final Answer:
The code word that represents "tough" in this language is fu.