Statements: A) Most of the route-64 buses go to my office. B) This is a route-64 bus. Conclusions: I) This bus goes to my office. II) This bus does not go to my office.

Introduction / Context:The premise uses a “most” quantifier, which indicates a majority but not totality. We must decide whether a specific instance (this particular route-64 bus) can be classified with certainty as going (or not going) to the office.

Given Data / Assumptions:

• “Most route-64 buses go to my office” means: more than half of all route-64 buses go to the office.
• “This is a route-64 bus” identifies a single instance within that population.

Concept / Approach:From “most,” we cannot deduce membership for a particular element without additional information. Certainty requires universal (“all”) or explicit identification. Therefore neither “goes” nor “does not go” is logically compelled.

Step-by-Step Solution:1) Conclusion I (“This bus goes to my office”) is plausible but not necessary; some route-64 buses do not go to the office.2) Conclusion II (“This bus does not go to my office”) contradicts the same plausibility; it is equally not necessary.3) Hence, neither I nor II follows with certainty.

Verification / Alternative check:A probability intuition (greater than 0.5) cannot replace logical necessity required in such problems.

Why Other Options Are Wrong:Any option selecting I or II asserts a definite outcome not guaranteed by a “most” statement.

Common Pitfalls:Confusing “most” with “all,” or treating high likelihood as logical entailment.

Final Answer:Both conclusions cannot be drawn.