Question:
The structure \( (N_3) \) satisfies the closure property, associativity and commutativity but the identity element 0 does not belong to \( N \).
The structure \( (N_3) \) satisfies the closure property, associativity and commutativity but the identity element 0 does not belong to \( N \).
Show Hint
A semi-group is an algebraic structure that satisfies the associative property without the need for an identity element.
Updated On: Jan 12, 2026
- \( \) quasi-group
- semi-group
- semi-group, non-group
- group
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Since the identity element does not exist for the group, it is classified as a semi-group.
Was this answer helpful?
0
0
Top Questions on Algebra
- A complex number 'z' satisfy both \(|z-6|=5\) & \(|z+2-6i|=5\) simultaneously. Find the value of \(z^3 + 3z^2 - 15z + 141\).
- Find the value of \[ \frac{6}{3^{26}} + 10\cdot\frac{1}{3^{25}} + 10\cdot\frac{2}{3^{24}} + \cdots + 10\cdot\frac{2^{24}}{3^{1}} : \]
- The sum of coefficients of \(x^{499}\) and \(x^{500}\) in the expression: \[ (1+x)^{1000} + x(1+x)^{999} + x^2(1+x)^{998} + \cdots + x^{1000} \] is:
- If \[ \sum_{r=1}^{25}\frac{r}{r^4+r^2+1}=\frac{p}{q}, \] where \(p\) and \(q\) are coprime positive integers, then \(p+q\) is equal to:
- Consider the 10 observations 2, 3, 5, 10, 11, 13, 15, 21, a and b such that mean of observation is a and variance is 34.2. Then the mean deviation about median, is :
View More Questions
Questions Asked in VITEEE exam
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Data Interpretation
- TUV : VYB :: PRA : ?
- VITEEE - 2025
- Odd one Out
- What is the pH of a solution with a \( \text{H}^+ \) concentration of \( 1 \times 10^{-3} \) mol/L?
- VITEEE - 2025
- Solubility Equilibria Of Sparingly Soluble Salts
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Odd one Out
- Find the odd one out from the following series: 5, 10, 20, 40, 100, 150, 200
- VITEEE - 2025
- Odd one Out
View More Questions