In this statement and conclusion reasoning question, two statements relate LED lights, bulbs, and tube lights. Accept the statements as true even if they differ from real electrical knowledge, then read the conclusions and decide which of them logically follow. Statements: (I) All LED are bulb. (II) Some bulbs are not tube light. Conclusions: (I) Some tube lights are LED. (II) All LED are tube lights.

Difficulty: Medium

Correct Answer: Neither conclusion (I) nor conclusion (II) follows

Explanation:


Introduction / Context:
This problem explores logical relationships among three categories: LED, bulbs, and tube lights. The statements describe how LED items and some bulbs relate to tube lights, and the conclusions speculate about LED objects that are tube lights. The test is whether you can avoid overinterpreting limited data and correctly identify which conclusions are not forced by the statements.


Given Data / Assumptions:

  • Statement (I): All LED are bulb.
  • Statement (II): Some bulbs are not tube light.
  • Conclusion (I): Some tube lights are LED.
  • Conclusion (II): All LED are tube lights.
  • We accept the statements as true and do not add any further facts about LED or tube lights.


Concept / Approach:
Statement (I) tells us that the set of LED is fully contained inside the set of bulbs. Statement (II) tells us that there exist some bulbs that are not tube lights. Important point: neither statement says that any bulb is a tube light or that any tube light is a bulb, nor do they link LED directly to tube lights. Therefore, any conclusion stating a definite relation between LED and tube lights needs strong justification. We test each conclusion by seeing whether we can draw a diagram satisfying the statements while making the conclusion false.


Step-by-Step Solution:
Step 1: Draw a large set for bulbs.Step 2: Place the LED set completely inside the bulbs set, because all LED are bulb.Step 3: Ensure that there is a region of bulbs that lies outside the tube lights set, because some bulbs are not tube lights. This is required by statement (II).Step 4: Notice that the statements say nothing about where tube lights lie relative to the LED region. Tube lights might partially overlap with bulbs, they might overlap with none of the LED bulbs, or they might even extend beyond bulbs.Step 5: Evaluate conclusion (I): “Some tube lights are LED.” This would require at least one object in the intersection of the tube lights set and the LED set. However, we can construct a valid diagram where tube lights overlap only with non LED bulbs or do not overlap with bulbs at all. In such a picture, none of the tube lights is an LED, yet both statements remain true. So conclusion (I) is not necessary.Step 6: Evaluate conclusion (II): “All LED are tube lights.” This requires that the LED region, which lies inside bulbs, also lies completely inside the tube lights set. But statement (II) explicitly guarantees the existence of some bulbs that are not tube lights. There is no rule that these non tube light bulbs cannot be LED. We can easily let all LED bulbs be in that non tube light region. Then no LED is a tube light, and conclusion (II) fails. Since this configuration still satisfies the given statements, conclusion (II) does not follow either.


Verification / Alternative check:
Consider a concrete scenario. Suppose there are 10 bulbs. Two of them are LED, and none of these LED bulbs are tube lights. Among the remaining 8 bulbs, some may be tube lights, and some may not. Additionally, imagine a separate set of tube lights that are not bulbs at all, or tube lights that are bulbs but not LED. This arrangement fulfills statement (I) because all LED are bulbs. It fulfills statement (II) because there are bulbs that are not tube lights. In this setup, no tube light is LED, and not all LED are tube lights. Thus both conclusions can fail while the statements are true.


Why Other Options Are Wrong:
Option A claims that only conclusion (I) follows, but we provided a valid situation where no tube light is an LED. Option B claims that only conclusion (II) follows, which is even less supported because statement (II) suggests some bulbs are not tube lights, and LED could easily be among those. Option D, which says both conclusions follow, clearly contradicts the counterexample. Only option C, which states that neither conclusion follows, fits the logical analysis.


Common Pitfalls:
Many students see “All LED are bulb” and “Some bulbs are not tube light” and intuitively think of real world lighting fixtures, then insert additional knowledge about how LED and tube lights work in practice. Logical reasoning questions require you to ignore such outside information. Another common mistake is to jump from “no information” to “some information,” for example, assuming that if nothing is said about LED tube lights, then some must exist.


Final Answer:
Therefore, the correct conclusion is that neither conclusion (I) nor conclusion (II) follows from the given statements.

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