I think I might have answered my own question. I will try to post a picture...


\\( f : P \rightarrow Q \\) and \\(g : P \leftarrow Q \\)

\\( g(q_1) = \bigvee \\{ p_1 \\} = p1 \\)

\\( g(q_{21}) = \bigvee \\{ p_1, p_{21}, p_{22}, p_{32}\\} = p_{32} \\)

\\( g(q_{22}) = \bigvee \\{ p_1, p_{21}, p_{22}, p_{31} \\} = p_{31} \\)