GATE | GATE-CS-2003 | Question 7

Consider the set ∑* of all strings over the alphabet ∑ = {0, 1}. ∑* with the concatenation operator for strings
(A) does not form a group
(B) forms a non-commutative group
(C) does not have a right identity element
(D) forms a group if the empty string is removed from ∑*

Answer: (A)

Explanation: The given set with the concatenation operator forms a Monoid as it follows the properties of Closure, Associativity and has an identity element(null string).
It is not a Group since no element has an inverse element i.e. there is no string S for another string R such that S*R = null string.

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