Question

Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________

(a) does not form a group

(b) does not have the right identity element

(c) forms a non-commutative group

(d) forms a group if the empty string is removed from

The question was posed to me by my school principal while I was bunking the class.

My question is from Groups topic in portion Groups of Discrete Mathematics

Answer 1

Right option is (a) does not form a group

The explanation: Identity element for concatenation is an empty string. Now, we cannot concatenate any string with a given string to get empty string there is no inverse for string concatenation. Only other 3 group properties such as closure, associative and existence of identity are satisfied.