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.