6. Each point on the circle with diameter $AB$ is colored one of red, yellow, or blue. It is known that $A$ and $B$ are colored red. Connecting points on the circle forms triangles. Given the following 4 conclusions:
(1) There must exist a right triangle with all three vertices colored red;
(2) There must exist a right triangle with all three vertices the same color;
(3) There must exist a right triangle with all three vertices different colors;
(4) There must exist a right triangle, either with all three vertices the same color or all three vertices different colors.
The number of true propositions is ( ) .
(A) 1
(B) 2
(C) 3
(D) 4
6.A.

It is known that connecting points on a circle forms a right-angled triangle if and only if the hypotenuse is the diameter. Now let's discuss the diameter.

If there are no red points on the circle other than points $A$ and $B$, then conclusion (1) does not hold; if there are no red points on the circle other than points $A$ and $B$, and the endpoints of all other diameters are of different colors (yellow and blue), then conclusion (2) does not hold; if the endpoints of all diameters on the circle are of the same color, then conclusion (3) does not hold.
Now we prove: Conclusion (4) holds.
If there are red points on the circle other than points $A$ and $B$, then there exists a right-angled triangle with three vertices of the same color (all red), and the proposition holds. If there are no red points on the circle other than points $A$ and $B$ (i.e., the remaining points on the circle are colored either yellow or blue), then draw a diameter $CD$. When the endpoints of $CD$ are of different colors, there exists a right-angled triangle with three vertices of different colors, and the proposition holds; when the endpoints of $CD$ are of the same color, let's assume they are both yellow. If there is a third yellow point at this time, then there exists a right-angled triangle with three vertices of the same color (all yellow), and the proposition holds. If there is no third yellow point at this time, i.e., all points on the circle except $A$, $B$, $C$, and $D$ are blue, then there exists a right-angled triangle with three vertices of the same color (all blue), and the proposition holds. In summary, conclusion (4) holds.