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If F is a free semigroup on a set S, then the concatenation of two even words is ________(a) a semigroup of F(b) a subgroup of F(c) monoid of F(d) cyclic group of FThis question was posed to me at a job interview.This is a very interesting question from Group Axioms topic in chapter Groups of Discrete Mathematics

Answer»

Right choice is (b) a subgroup of F

The explanation is: Let F be the free semigroup on the set S = {m,n}. Let, E consist of all even words, i.e, words with even LENGTH and the CONCATENATION of two such words is ALSO even. Thus E is a SUBSEMIGROUP of F.



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