  In this paper, we study $Z_2$ actions on a cell complex X having the
cohomology ring isomorphic to that of the wedge sum $P^2 (n) V S^{3n}$ or $S^n
V S^{2n} V S^{3n}$. We determine the possible fixed point sets depending on
whether or not X is totally non-homologous to zero in $X_{Z_2}$ and give
examples realizing the possible cases.
