1. (19 marks) Short-answer questions (a) (6 marks) True or false? No explanation is needed i. For all languages L, if L can be decided in polynomial time by some Turing machine, then L can be accepted by some pushdown automaton ii. For all languages L, if there is a finite automaton that accepts L, then there is a context-free grammar that generates L iii. For all languages L, if there is a non-deterministic three-tape Turing machine that accepts L, then there is a deterministic, one-tape Turing machine that accepts L (b) (2 marks) Provide an example of languages L1 and L2 such that L1 C L2, L2 is context-free, but L1 is not context-free