(c) For the following question part you may assume the following true fact as given: Fact: Given an NFA D = (Q1, 2, 81,9

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C For The Following Question Part You May Assume The Following True Fact As Given Fact Given An Nfa D Q1 2 81 9 1 (58.78 KiB) Viewed 57 times

(c) For the following question part you may assume the following true fact as given: Fact: Given an NFA D = (Q1, 2, 81,90, Fi) that recognises language B and an NFA D2 = (Q2, 2, 82, ro, F2) that recog- nises language C, there is a way to construct an NFA that recognises BNC (i) Show that the following statement is true: For any languages B, C, if there is a regular expression representing B and a regular expression representing C then there is a regular erpression representing Bnc. You must justify your answer, clearly stating in full any results from the lecture notes that you rely on in your explanation. (Facts used that were given in the lecture notes may be stated without reproducing their proof.) [5] (ii) Prove, by induction on i, that the following statement is true for all i > 1: For any languages A1, A2, ..., Aj, if there are regular er- pressions describing each of them, then there is a regular expression describing An An...NA.