Statements and conclusions – buttons, switches and connectors: Statement I: Some buttons are switches. Statement II: All buttons are connectors. Conclusions: I. Some switches are connectors. II. Some connectors are buttons.

Introduction / Context:
This question is another set-based reasoning problem involving buttons, switches and connectors. You are given one statement describing a partial overlap (“some buttons are switches”) and another stating a full inclusion (“all buttons are connectors”). You must decide which of the conclusions about switches and connectors logically follow.

Given Data / Assumptions:

Statement I: Some buttons are switches (at least one object is both a button and a switch).
Statement II: All buttons are connectors (Buttons ⊂ Connectors).
Conclusion I: Some switches are connectors.
Conclusion II: Some connectors are buttons.
We assume that buttons exist and all statements are true.

Concept / Approach:
We will use basic set logic. If some buttons are switches and all buttons are connectors, then those particular buttons that are switches must also be connectors. This will help us with Conclusion I. For Conclusion II, we notice that if all buttons are connectors and there are buttons, then automatically some connectors are buttons.

Step-by-Step Solution:
From Statement I, there is at least one element that belongs to both the sets “buttons” and “switches”. From Statement II, every button is a connector. Therefore, that specific element (button ∧ switch) is also a connector. Thus, we have at least one element that is both a switch and a connector. Therefore, Conclusion I, “Some switches are connectors,” is true. Now look at Conclusion II: “Some connectors are buttons.” From Statement II again, all buttons are connectors. This means the entire set of buttons lies inside the set of connectors. Since we know there are some buttons (from Statement I, because some buttons are switches), it follows that at least some connectors are buttons. Thus, Conclusion II is also true.

Verification / Alternative check:
Draw a simple Venn diagram: draw a large circle for connectors. Inside it, draw a smaller circle for buttons (since all buttons are connectors). Mark a region overlapping between the buttons circle and another circle for switches, representing the “some buttons are switches” statement. This overlap region is automatically inside the connectors circle, which shows that some switches are connectors and some connectors are buttons. Both conclusions are clearly supported.

Why Other Options Are Wrong:
Saying only one conclusion follows ignores the direct set relationships that support both. Saying neither follows conflicts with the clear implications of the statements. The idea that we “cannot determine which” is also incorrect, because a straightforward set diagram shows that both are valid consequences.

Common Pitfalls:
A common pitfall is to underuse the fact that buttons exist, which is implied by “some buttons are switches.” If there were no buttons, the first statement would be false. Another mistake is to forget that when one set is fully contained in another, the larger set must include at least some members of the smaller set (assuming it is non-empty), which is the basis for Conclusion II.

Final Answer:
Both conclusions are logically valid. The correct option is Both conclusions I and II follow.