In the question given below, three conclusions are given followed by five statements. You have to choose the correct set of statements that logically satisfies the given conclusions disregarding the commonly known facts. Conclusions: I. Some atoms being matter is a possibility. II. Few elements are not particles. III. No matter is molecules. Statements: I. Every molecules are atoms. No matter is particle. Only a few elements are matter. Some particles are not molecules. II. None of the particles are molecules. Half elements are molecules. All matter are atoms. Some atoms are particles. III. Not a single matter is particle. Only a few elements are matter. All atoms are elements. Very few molecules are particles. IV. All molecules are Atoms. All matter are atoms. Some particles are elements. No element is molecule. V. Some particles are molecules. Only a few matter are elements. No particle is atom. Each atom is element.

### Concept & Logic This is a reverse syllogism problem where we must test each statement set to see if it makes ALL the given conclusions logically follow. For a definitive negative conclusion like "No matter is molecules" to be true, the statement must guarantee that the two sets have zero intersection: $$ \text{Matter} \cap \text{Molecules} = \emptyset $$ ### Step-by-Step Solution Let's test the given statements to see if they satisfy Conclusion III: "No matter is molecules." * **Statement I:** We are given "Every molecules are atoms" and "No matter is particle". There is no direct or indirect negative relation established between matter and molecules. They could still overlap. Conclusion III does not logically follow. * **Statement II:** We are given "None of the particles are molecules" and "All matter are atoms." Matter is not constrained to be particles, so it can still intersect with molecules. Conclusion III does not logically follow. * **Statement III:** "Not a single matter is particle" and "Very few molecules are particles." This proves that the molecules which are particles cannot be matter ("Some molecules are not matter"). However, it does *not* prove that *no* matter is molecules. The remaining molecules could be matter. Conclusion III does not logically follow. * **Statement IV:** "All matter are atoms" and "All molecules are Atoms." Both sets are subsets of Atoms and can freely overlap within that larger set. Conclusion III does not logically follow. * **Statement V:** There is no negative premise provided that logically completely separates all matter from all molecules. Conclusion III does not logically follow. Since none of the five statements can logically satisfy Conclusion III, we do not even need to check Conclusions I and II. ### Exam Strategy & Shortcut Always scan the conclusions for the most definitive, restrictive statement—in this case, the universal negative "No matter is molecules." Instead of drawing complex Venn diagrams for all 5 statements, quickly scan each statement specifically looking for a negative link (like `No A is B`) connecting `matter` and `molecules`. Since no statement creates a complete separation between them, you can confidently eliminate all options and choose "None of the statements satisfy" in under a minute. ### Common Pitfall Students often confuse "Some A are not B" with "No A is B." For example, in Statement III, deducing that *some* molecules (the ones that are particles) are not matter does NOT mean that *all* matter is separated from molecules. ### Final Answer Therefore, the correct answer is **None of the statements satisfy**.