Determine whether or not the definition of * given below gives a … - Vidyadip

Question

Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $R,$ define by $a * b = ab^2.$
Here, $Z^+$ denotes the set of all non-negative integers.

✓

Answer

$\text{a, b}\in\text{R}$Implies that $\text{a, b}^2\in\text{R}$
Implies that $\text{ab}^2\in\text{R}$
Implies that $\text{a}\ ^*\ \text{b}\in\text{R}$
Thus, $*$ is a binary operation on $R$.

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 RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following:
$\sec^{-1}\Big\{\sec\Big(-\frac{7\pi}{3}\Big)\Big\}$

Compute the indicated products.$\left[\begin{array}{rrr} {3} & {-1} & {3} \\ {-1} & {0} & {2} \end{array}\right]\left[\begin{array}{rr} {2} & {-3} \\ {1} & {0} \\ {3} & {1} \end{array}\right]$

Find the integral: $\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$

Find the value $k$, so that the given function is continuous at $x=5$
$
f(x)=\left\{\begin{array}{ccc}
k x+1 & \text { if } & x \leq 5 \\
3 x-5 & \text { if } & x>5
\end{array}\right.
$

Evaluate the following integrals:
$\int\limits^3_2\frac{1}{\text{x}}\text{ dx}$

Find the value of $\int \frac{\sin 2 x}{a \sin ^2 x+b \cos ^2 x} d x$.

Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.

If $A$ is a square matrix of order $3$ with determinant $4,$ then write the value of $|-A|.$

A man $1.6m$ tall walks at the rate of $0.3\ m/s$ away from a street light is $4 m$ above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

Evaluate the following definite integrals:
$\int_{-2}^\limits{3}\frac{1}{\text{x}+7} \text{ dx}$