Question

I know how to do a) and b) but unsure about c)

Question 3. (5 marks) A language L is defined over a set of three letters {a, b, c}. A string ordering matters (i.e. "abc" is not equal to "bca"). The length of a string is the number of letters the string contains. For example, "abc" has length 3 a sequence of letters where (a) How many strings of length 4 can you create? [1 mark] (b) How many strings of length 4 do not have consecutive characters being the same? [1 mark] (c) How many strings of length 4 contain neither "cab" nor "bac", or do not have consecutive characters being the same? [3 marks] Do not list out the answers exhaustively

c) Number of strings that (do not not contain "cab" or "bac" BUT may contain repeated consecutive letters), OR (strings that do not contain repeated consecutive letters but may contain "cab" or "bac").

Answer 1

three eter ifa,b,cf Set fo,besfa,te, e b 9epea lid one of tho e Her cam For each et, no. ngs thal can be ereali 4 24 rng tha!" can be erealid enth 3x4! Therefore, total mo 2x24 = 12 DaxA! each imce there asee 3 kelk can ereal 4 ring singls Letir Therefore, there are "thtal 3 trings ntainang eab' Jet acab beab, ceab cont the re are epac' abae, bbaa, cbac No. ringf angth 4thar contain eab' nor neithur = 72-3- 3 72-6 Nov, for et fa, b, e, a te ud eonzide 'na 16 a Ahe 4iongle leter strings containing conseutire 2x3 - 2r6 =12

23! Smee, a a' aam geaoralo ts am b prealif can Limitanty for etaheandfasb,e, each set h lain 12 ktrngstha have Consecutive sarne leter A.Aring Layth 4thal do not hare ae conpetive charooterbeing the - 2-(3x12) 2-36 -36 ringe unyth 4-thal Therufere no do not have contain neither cab' n eonsecertive aharracters being-the pame Lat36 02

Only the solution of (c) is provided.

For any doubt comment below.