# Constructing a Push Down Automaton

Given a 7 tuple push down automaton

M = (K, Σ, Γ, Δ, s, F) where K = {p, q, r}, Σ = {a, b, c}, Γ = {a}, s = p, and F = {r}, with the transitions

((p, b, ε), (q, ε)), ((q, a, e,), (p, a)), ((p, c, a), (r, ε)), ((r, c, a), (r, ε))

This is my diagram:

How can I account for the last element of the stack? Some other examples saw had something like ε, ε -> $ in the first state to second, and then ε, $ -> ε for the final.