Logical consistency – Which of the following statements is certainly true (independent claims)? I. “All players are not tall” (i.e., not all players are tall). II. All basketball players are tall. III. All tall people are players. IV. Some players are tall.

Introduction / Context:
The task is to identify which single claim can be accepted as universally valid without depending on the truth of the others. Items I–III are universal or quasi-universal claims and are easy to defeat by counterexample; item IV is existential and aligns with general real-world plausibility in aptitude settings.

Given Data / Assumptions:

• The items are independent statements; we are not to combine them as premises.
• “All players are not tall” is typically read in tests as “Not all players are tall”.

Concept / Approach:
To be “certainly true,” a statement must hold across reasonable interpretations and avoid over-generalization. Claims II and III are sweeping universals and can be false in many natural models. Claim I is a particular style ambiguity and is not guaranteed. Claim IV (“Some players are tall”) is mild and matches everyday knowledge, and is the only one commonly accepted as “true” in such question forms.

Step-by-Step Solution:
Provide a counterexample to II: a short basketball player would falsify it.Provide a counterexample to III: a tall non-player falsifies it.Ambiguity in I prevents certainty.IV states an existential fact consistent with the domain: there exist tall players; this is overwhelmingly safe and intended as the test key.

Verification / Alternative check:
In standardized syllogism practice, when faced with one natural existential and several sweeping universals lacking support, the existential is chosen as the certain truth.

Why Other Options Are Wrong:
They assert universals without premise support and are easily refuted.

Common Pitfalls:
Reading I as “All players are tall” (the opposite) or treating the set of tall people as identical to players.

Final Answer:
IV.