Aptitude
March 19, 2025GATE 2003
March 19, 2025GATE 2003
|
Question 7
|
Consider the set ∑* of all strings over the alphabet ∑ = {0, 1}. ∑* with the concatenation operator for strings
|
does not form a group
|
|
|
forms a non-commutative group
|
|
|
does not have a right identity element
|
|
|
forms a group if the empty string is removed from Σ*
|
Question 7 Explanation:
In the concatenation ‘∊’ is the identity element. And given one is not a group because no element has inverse element.
→ To perform concatenation with the given set can result a Monoid and it follows the property of closure, associativity and consists of identity element.
→ To perform concatenation with the given set can result a Monoid and it follows the property of closure, associativity and consists of identity element.
Correct Answer: A
Question 7 Explanation:
In the concatenation ‘∊’ is the identity element. And given one is not a group because no element has inverse element.
→ To perform concatenation with the given set can result a Monoid and it follows the property of closure, associativity and consists of identity element.
→ To perform concatenation with the given set can result a Monoid and it follows the property of closure, associativity and consists of identity element.