Six people and a social triangle

1. It is symmetrical to the previous case: either a triangle of unknowns appears with
2. Choose any person X. He or she is related to 5 other people.
3. Yes, there is always one of the two triangles (known or unknown).

Back to the problem
Answer: Yes, there is always one of the two triangles (known or unknown).
Choose any person $X$. He has a relationship with 5 other people.
Each relationship is of two types: “knows” or “does not know.”
By pigeon, among those 5 relationships at least 3 are of the same type.
Case 1: $X$ meets $A,B,C$.

• If between $A,B,C$ there is a couple that knows each other (for example $A$ and $B$), then $X,A,B$ form an acquaintance triangle.
• If there are no couples who know each other, then $A,B,C$ are strangers' triangle.

Case 2: $X$ does not know $A,B,C$.
It is symmetrical to the previous case: either a triangle of strangers appears with $X$, or a triangle of acquaintances appears within $A,B,C$.
In all cases, one of the two triangles exists.