Consider a 3^(5-2) design with D = ABC and E = A^2BC. (a) Find its defining contrast subgroup. What is the resolution?

Consider a 3^(5-2) design with D = ABC and E = A^2BC.

1. (a) Find its defining contrast subgroup. What is the resolution?
2. (b) There are 3^(2 -1) effects aliased with the main effect of A. Find them.
3. (c) Find all the aliasing relations between main effects and two-factor interaction components (ignoring 3-factor interactions or higher).
4. (d) Identify the clear main e↵ects and clear two-factor interaction component if they exist.