Statements and conclusions – envelopes, gums, seals and adhesives: Statements: Some envelopes are gums. Some gums are seals. Some seals are adhesives. Conclusions: 1. Some envelopes are seals. 2. Some gums are adhesives. 3. Some adhesives are seals. 4. Some adhesives are gums.

Introduction / Context:
This is a logical reasoning question involving partial overlaps between sets: envelopes, gums, seals and adhesives. You are asked which conclusions must follow. The challenge is that the statements only guarantee some specific overlaps, not full inclusions or complete chains. You must therefore check which of the conclusions are forced by the information and which are merely possible but not necessary.

Given Data / Assumptions:

Some envelopes are gums (E ∩ G ≠ ∅).
Some gums are seals (G ∩ S ≠ ∅).
Some seals are adhesives (S ∩ A ≠ ∅).
Conclusions: 1. Some envelopes are seals (E ∩ S ≠ ∅).
2. Some gums are adhesives (G ∩ A ≠ ∅).
3. Some adhesives are seals (A ∩ S ≠ ∅).
4. Some adhesives are gums (A ∩ G ≠ ∅).

Concept / Approach:
“Some X are Y” simply tells us that the intersection of sets X and Y is non-empty. However, having overlaps in a chain like E–G and G–S does not guarantee an overlap between E and S unless explicitly stated. Similarly, having G–S and S–A does not force G–A or E–A overlaps. We must be careful not to assume transitivity for “some” relationships where it does not necessarily hold.

Step-by-Step Solution:
From the third statement, “Some seals are adhesives,” we know directly that there is at least one object that is both a seal and an adhesive. Therefore, Conclusion 3, “Some adhesives are seals,” is simply a restatement of this and must be true. Now consider Conclusion 1: “Some envelopes are seals.” We know some envelopes are gums and some gums are seals. It is possible that the envelopes that are gums are different from the gums that are seals; the sets may overlap in different regions. For example, one group of gums could be used on envelopes but never as seals, while another group of gums may be used in seals but never on envelopes. In that case, there is no envelope that is also a seal, while all statements remain true. Therefore, Conclusion 1 does not necessarily follow. Consider Conclusion 2: “Some gums are adhesives.” We know some gums are seals and some seals are adhesives, but it is not guaranteed that the same seals that are adhesives are the ones that are gums. Thus there may be no object that is both gum and adhesive, even though all statements are satisfied. So Conclusion 2 does not necessarily follow. Consider Conclusion 4: “Some adhesives are gums.” This would require an overlap between adhesives and gums, which again is not assured by the given information. The adhesives that are seals might be completely disjoint from gums. Hence, Conclusion 4 also does not necessarily follow.

Verification / Alternative check:
To confirm, build a model: imagine three separate pairs of overlapping sets—envelopes with one part of gums, gums with some seals, and seals with some adhesives. Arrange them so that these overlaps do not coincide. In such a diagram, statements about some envelopes being gums, some gums being seals, and some seals being adhesives are true, but there is no envelope that is a seal, no gum that is an adhesive and no adhesive that is a gum. Only the direct overlap between seals and adhesives is guaranteed, capturing Conclusion 3.

Why Other Options Are Wrong:
Choosing any conclusion other than 3 as necessarily true relies on an unjustified assumption that “some” overlaps automatically chain through multiple sets. The option stating that both 1 and 3 follow is wrong because 1 can be false in a valid scenario. Options pointing to 1, 2 or 4 alone ignore the fact that they are not logically forced by the statements.

Common Pitfalls:
A common mistake is to treat “some A are B” statements as if they were universal and to assume transitivity. Remember that a partial overlap between A and B and another between B and C does not guarantee any overlap between A and C. Constructing counterexamples in your mind or on paper is an effective way to avoid this trap.

Final Answer:
Only Conclusion 3 (“Some adhesives are seals”) is guaranteed by the given statements. The correct option is Only conclusion 3 follows.