D. a-iv, b-iii, c-i, d-ii
Decomposition rule: If $x->y z$ then $x->y, x->z$
Union rule: If $x->y, x->z$ then $x->y z$
Composition rule: if $x->y$ and $z->w$ then $x z->y w$
Pseudo transitivity rule : If $\mathrm{x}->\mathrm{y}$ and $\mathrm{yw}->\mathrm{z}$ then $\mathrm{xw}->\mathrm{z}[\mathrm{y}$ replace by x$]$.
X $\rightarrow$ Zhen
