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Discrete Math

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so i have this description: S consists of all strings of a's, b's and c's where an increasing number of a's come before an increasing number of b's and c's or c's and b's. does this make sense for this recursive definition of the set S over {a,b,c}: 1. a is in S and 2. if x in S then ax, xb, xc are in S?

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