Download App

Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations2 Marks
Question
Determine whether the following operations define a binary operation on the given set or not:
$'*\ ' $ on $ N$ defined by $a * b = a^b$ for all $\text{a, b}\in\text{N.}$
✓

Answer

Let $\text{a, b}\in\text{N}$
Then, $\text{a}^{\text{b}}\in\text{N}$ $\big[$Therefore $\text{a}^{\text{b}}\neq0$ and $a^b$ is positive integer$\big]$
Implies that $\text{a}\ ^*\ \text{b}\in\text{N}$
Therefore, $\text{a}\ ^*\ \text{b}\in\text{N},\ \forall\ \text{a, b}\in\text{N}$
Thus, $*$ is a binary operation on $N.$

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

Explore more

More "2 Marks Questions" from Binary Operations→Binary Operations — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
→
If $\begin{vmatrix}2\text{x}+5&3\\5\text{x}+2&9\end{vmatrix}=0,$ find x.
→
Write the value of $\sin^{-1}(\sin1550^\circ).$
→
Differentiate the $\log(\cos e^x)$ w.r.t. x.
→
Write a value of $\int\sin^3\text{x}\cos\text{x dx}$
→
The probability distribution function oif a random variable $X$ is given by
$X_i$ $0$ $1$ $2$
$P_i$ $3c^3$ $4c - 10c^2$ $5c - 1$
Where $c > 0$
Find: $c.$
→
Find the angle between two vectors $\vec a$ and $\vec b$ with magnitudes $\sqrt 3 $ and 2, respectively, having $\vec a\;.\vec b = \sqrt 6 $
→
Define identity element for a binary operation defined on a set.
→
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the values of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.
→
Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.
→