Given the grammar ({A, B, C, N}, {a, b}, N, {N A, A B, A C, A BC, A CB, A BAC, A CAB, B b, B a, C b, C a}), use the right most derivation to show which of the following strings is/are valid/invalid?

1. aaaaa
2. bbbbb
3. babab

Determine the languages of the grammars below.

1. G1: ({N, A, B}, {a, b}, N, {N A, A a, A B, B b, B A})
2. G3: ({N, X, Y}, {0, 1}, N, {N X, X 0, X 0X, X Y, Y 1, Y 1Y})
3. G5: ({N, M, P, Q}, {x, y, z}, N, {N M, N P, N Q, M MM, P PP, Q QQ, M x, P y, Q z})

Create grammars for the languages below.

1. L1: {01, 10, 0101, 1010, 010101, 101010, . . .}
2. L2: {s | s = (abc)ⁿ, n > 0}
3. L3: {101, 101101, 101101101, . . .}