Doubt in Syllogism Conclusion (Conclusion B) Statements given: No black is orange All yellow is orange Some y…

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• KG AI MentorKG AI Mentor9 Feb 2026

  Great question — this is a common point of confusion in syllogism reasoning, especially when it comes to possibility-based conclusions. Let’s break it down carefully. --- Given Statements:No black is orange → Black and Orange are disjoint sets. → No overlap. All yellow is orange → Yellow ⊆ Orange → Every yellow is orange, but not necessarily vice versa. Some yellow is green → There is an overlap between Yellow and Green. → Some yellow things are green. All green is pink → Green ⊆ Pink --- Conclusions:#### A) Some orange are pink Let’s trace the chain: Some yellow is green → So, some green exists. All green is pink → So, that some green is pink. Some yellow is green → So, some yellow is pink. All yellow is orange → So, that some yellow (which is pink) is also orange. → Therefore, some pink is orange → i.e., some orange are pink. ✅ Conclusion A is valid. --- #### B) All orange being yellow is a possibility This is a possibility conclusion — not a definite one. You're right that "All yellow is orange" does not imply "All orange is yellow" — that would be a logical fallacy (converting a universal affirmative). But here’s the key: > "All orange being yellow is a possibility" means: > Is it logically possible that every orange is yellow? > Not that it must be true — just that it could be true without contradicting the given statements. Let’s analyze: We know: All yellow is orange → So, Yellow ⊆ Orange But we don’t know if Orange ⊆ Yellow — that would be the reverse. Now, can all orange be yellow? That would mean: Orange = Yellow (since Yellow ⊆ Orange, and if Orange ⊆ Yellow, then they are equal). Is this possible given the statements? The statements do not say that there are oranges that are not yellow. They only say: All yellow is orange — so orange could be larger than yellow, or equal to yellow. So, if all orange is yellow, then: All yellow is orange → OK (since they are equal) No black is orange → OK Some yellow is green → OK All green is pink → OK There is no contradiction in assuming that all orange is yellow. Therefore, "All orange being yellow" is a possibility — even though it's not necessarily true. ✅ Conclusion B is valid — because it's possible, not required. --- #### C) Some green is not black Let’s see: All green is pink → Green ⊆ Pink Some yellow is green → So, some green exists No black is orange → But green is not necessarily related to black directly. But we know: Green → Pink Yellow → Orange Some yellow is green → So, some green is yellow → so some green is orange But no black is orange → So, no black can be orange But green is part of orange (via yellow) → So, some green is orange → So, that green is not black (since no black is orange) Therefore, some green is not black → because some green is orange, and nothing black is orange. ✅ Conclusion C is valid. --- ✅ Final Answer: All conclusions follow.--- 🔍 Why is B valid despite the reverse not being logically valid?Because "possibility" in syllogism means: > "Is there a scenario where this could be true, without contradicting the premises?" Even though "All orange is yellow" is not logically entailed by "All yellow is orange", it is not ruled out by the premises. So, it is possible that all orange is yellow — just not certain. This is a key distinction in syllogism: Definite conclusions must follow necessarily. Possibility conclusions only need to be not ruled out. --- 🧠 Summary:| Conclusion | Valid? | Reason | |----------|--------|--------| | A) Some orange are pink | ✅ Yes | Chain: Yellow → Green → Pink, and Yellow ⊆ Orange | | B) All orange being yellow is a possibility | ✅ Yes | Not contradicted; possible if Orange = Yellow | | C) Some green is not black | ✅ Yes | Some green is orange → no black is orange → so that green is not black | --- ✅ Final Answer: All conclusions follow.Your doubt is understandable — but possibility conclusions are about logical consistency, not logical necessity. So, B is valid — because it's possible, not required. Hope this clears it up! — KG AI Mentor 🤖

• Deepika Gupta22 Oct 2025

  @kg_617024 All orange being yellow is a possibility is true .. all are true please have a look on this img