Class 12 Mathematics Relation and Function Binary Operation

Medium

Consider a binary operation $$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table. Compute $(2 \,^ \,3) \,^* \,4$ and $2 \,^* \,(3 \,^* \,4)$.

$^*$ $1$ $2$ $3$ $4$ $5$

$1$ $1$ $1$ $1$ $1$ $1$

$2$ $1$ $2$ $2$ $2$ $2$

$3$ $1$ $2$ $3$ $3$ $3$

$4$ $1$ $2$ $3$ $4$ $4$

$5$ $1$ $2$ $3$ $4$ $5$

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Vedclass pdf generator app on play store

Solution

(N/A) To compute $(2 \,^* \,3) \,^* \,4$:
From the table,$2 \,^* \,3 = 2$.
Then,$(2 \,^* \,3) \,^* \,4 = 2 \,^* \,4 = 2$.
To compute $2 \,^* \,(3 \,^* \,4)$:
From the table,$3 \,^* \,4 = 3$.
Then,$2 \,^* \,(3 \,^* \,4) = 2 \,^* \,3 = 2$.

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Relation and Function

Subtopic

Binary Operation

Let $^$ be the binary operation on $N$ given by $a \,^ \,b = \text{L.C.M. of } a \text{ and } b$. Find $5 \,^* \,7$ and $20 \,^* \,16$.

Medium

View Solution

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a \,^ \,b = a^{2} + b^{2}$. Which of the following is true?

Medium

View Solution

Let $$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a b = (a - b)^{2}$ for all $a, b \in Q$ is commutative.

Medium

View Solution

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a ^ b = a - b$. Determine whether the operation $^*$ is commutative and associative.

Medium

View Solution

Define a binary operation $^$ on the set $\{0, 1, 2, 3, 4, 5\}$ as $a \,^ \, b = \begin{cases} a+b, & \text{If } a+b < 6 \\ a+b-6, & \text{If } a+b \geq 6 \end{cases}$. Show that $0$ is the identity for this operation and each element $a \neq 0$ of the set is invertible with $6-a$ being the inverse of $a$.

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$^*$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$2$	$2$	$2$
$3$	$1$	$2$	$3$	$3$	$3$
$4$	$1$	$2$	$3$	$4$	$4$
$5$	$1$	$2$	$3$	$4$	$5$

Similar Questions

Let $^*$ be the binary operation on $N$ given by $a \,^* \,b = \text{L.C.M. of } a \text{ and } b$. Find $5 \,^* \,7$ and $20 \,^* \,16$.

Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a \,^* \,b = a^{2} + b^{2}$. Which of the following is true?

Let $*$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a * b = (a - b)^{2}$ for all $a, b \in Q$ is commutative.

Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a ^* b = a - b$. Determine whether the operation $^*$ is commutative and associative.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let $^$ be the binary operation on $N$ given by $a \,^ \,b = \text{L.C.M. of } a \text{ and } b$. Find $5 \,^* \,7$ and $20 \,^* \,16$.

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a \,^ \,b = a^{2} + b^{2}$. Which of the following is true?

Let $$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a b = (a - b)^{2}$ for all $a, b \in Q$ is commutative.

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a ^ b = a - b$. Determine whether the operation $^*$ is commutative and associative.