Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements:
All polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.

Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.

Both conclusions I and III follow