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:
The determinant $\begin{vmatrix}\sin\text{A}&\cos\text{A}&\sin\text{A}+\cos\text{B}\\\sin\text{B}&\cos\text{A}&\sin\text{B}+\cos\text{B}\\\sin\text{C}&\cos\text{A}&\sin\text{C}+\cos\text{B}\end{vmatrix}$ is equal to zero.
Two collinear vectors having the same magnitude are equal.
State True or False for the statements:
If A and B are independent, then.
P (exactly one of A, B occurs) = P(A)P(B') + P(B)P(A')
Which of the following statements are True or False.
A matrix denotes a number.
Which of the following statements are True or False.
AA′ is always a symmetric matrix for any matrix A.
State True or False for the following:
Differential equation representing the family of curves $\text{y}=\text{e}^{\text{x}}(\text{A}\cos\text{x}+\text{B}\sin\text{x})$ is $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}-2\frac{\text{dy}}{\text{dx}}+2\text{y}=0.$
State True or False for the statements of the following Exercise:
The maximum value of $\begin{vmatrix}1&1&1\\1&1+\sin\theta&1\\1&1&1+\cos\theta\end{vmatrix}$ is $\frac{1}{2}.$
State True or False for the statements:
Rolle’s theorem is applicable for the function f(x) = |x - 1| in [0, 2].
State True or False for the following:
The unit vector normal to the plane x + 2y +3z – 6 = 0 is $\frac{1}{\sqrt{14}}\hat{\text{i}}+\frac{2}{\sqrt{14}}\hat{\text{j}}+\frac{3}{\sqrt{14}}\hat{\text{k}}.$
Which of the following statements are True or False.
$(AB)^{-1} = A^{-1}. B^{-1},$ where $A$ and $B$ are invertible matrices satisfying commutative property with respect to multiplication.