Categorical logic – color and features of “Signots” and “Lamels” Given: All Lamels are Signots with buttons. No yellow Signots have buttons. Question: If those two facts are true, is the statement “No Lamels are yellow” true, false, or uncertain?

Introduction / Context:
This syllogism mixes class membership (Lamels are Signots) with an attribute (having buttons) and a color constraint (yellow Signots lack buttons). We test whether a universal exclusion follows.

Given Data / Assumptions:

• S1: All Lamels are Signots with buttons (Lamels ⊆ Signots ∩ Buttons).
• S2: No yellow Signots have buttons (Yellow ∩ Signots ⇒ not Buttons).
• Claim to evaluate: No Lamels are yellow.

Concept / Approach:
If every Lamel is a Signot that has buttons, and no yellow Signot has buttons, then a Lamel cannot be a yellow Signot because that would contradict “has buttons.” Therefore, Lamels must be non-yellow.

Step-by-Step Solution:
1) From S1: For any x, if x is Lamel ⇒ x is Signot and x has Buttons.2) From S2: For any x, if x is Yellow and x is Signot ⇒ x does not have Buttons.3) Suppose, for contradiction, some Lamel is Yellow: then it is a Yellow Signot with Buttons and without Buttons simultaneously, impossible.4) Hence, no Lamel is Yellow ⇒ statement is True.

Verification / Alternative check:
Venn-style reasoning: Lamels live entirely within the “Signots with buttons” region, while yellow Signots live entirely outside the “with buttons” region; the sets cannot overlap.

Why Other Options Are Wrong:

• False / Uncertain: The logical exclusion is compelled by the premises; no ambiguity remains.
• Both true and false: Not applicable in a consistent model.

Common Pitfalls:
Confusing “No yellow Signots have buttons” with “No Signots have buttons.” The color qualifier is essential; combined with S1, it still excludes yellow Lamels.

Final Answer:
True