5. Let ? = {a, b, c}. For each of the following, construct a context free grammar G such that
(a) L(G) = {a$^i$b$^j$c$^k$ ? ?* | i, j, k ? N, j = i + k}
(b) L(G) = {a$^i$b$^j$c$^k$ ? ?* | i, j, k ? N, i = j or i = k}
(c) L(G) = {a$^i$b$^j$c$^k$ ? ?* | i, j, k ? N, i < j or i > k}
(d) L(G) = {a$^i$b$^j$ ? ?* | i, j ? N, i ? j ? 2i}