Question
State True or False for the statements.
A binary operation on a set has always the identity element.

Answer

False.
Solution:
‘+’ is a binary operation on the set N but it has no identity element.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

State True or False for the statements of the following Exercise:
Let $ \begin{vmatrix}\text{a}&\text{p}&\text{x}\\\text{b}&\text{q}&\text{y}\\\text{c}&\text{r}&\text{z}\end{vmatrix}=16,$ then $\Delta_1=\begin{vmatrix}\text{p}+\text{x}&\text{a}+\text{x}&\text{a}+\text{p}\\\text{q}+\text{y}&\text{b} +\text{y}&\text{b}+\text{q}\\\text{r}+\text{z}&\text{c}+ \text{z}&\text{c}+\text{r}\end{vmatrix}=32.$
Zero vector is unique.
State True or False for the statements of the following Exercise:
$\big(\text{A}^3\big)^{-1}=(\text{A}^{-1})^3,$ where A is square matrx and |A| ≠ 0.
Two collinear vectors are always equal in magnitude.
State True or False for the statements:
The composition of two continuous function is a continuous function.
State True or False for the following:
Correct substitution for the solution of the differential equation of the type $\frac{\text{dy}}{\text{dx}}=({\text{x}},\text{y}),$ where f(x, y) is a homogeneous function of zero degree is y = vx.
State True or False for the statements of the following Exercise:
If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.
State True or False for the statements:
If A and B are mutually exclusive events, then they will be independent also.
State True or False for the following:
The vector equation of the line $\frac{\text{x}-5}{3}=\frac{\text{y}-4}{7}=\frac{\text{z}-6}{2}$ is $\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda(3\hat{\text{i}}-7\hat{\text{j}}+2\hat{\text{k}}).$
Which of the following statements are True or False.
If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.