Class 12 Mathematics Relations and Functions 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 $2 \,^* \,(3 \,^* \,4)$.

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

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

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

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

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

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

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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,$2 \,^* \,(3 \,^* \,4) = 2 \,^* \,3 = 2$.

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Class 12 Questions

Class 12

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Relations and Functions

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Binary Operation

Show that $: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ defined by $a b = a + 2b$ is not commutative.

Medium

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Show that the $\vee: R \times R \rightarrow R$ given by $(a, b) \rightarrow \max\{a, b\}$ and the $\wedge: R \times R \rightarrow R$ given by $(a, b) \rightarrow \min\{a, b\}$ are binary operations.

Medium

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Determine whether or not each of the definitions of $$ given below gives a binary operation. In the event that $$ is not a binary operation,give justification for this. On $Z^{+}$,define $$ by $a b = a$.

Medium

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Consider a binary operation $$ on $N$ defined as $a b = a^{3} + b^{3}$. Choose the correct answer.

Medium

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

Medium

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

Similar Questions

Show that $*: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ defined by $a * b = a + 2b$ is not commutative.

Show that the $\vee: R \times R \rightarrow R$ given by $(a, b) \rightarrow \max\{a, b\}$ and the $\wedge: R \times R \rightarrow R$ given by $(a, b) \rightarrow \min\{a, b\}$ are binary operations.

Determine whether or not each of the definitions of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation,give justification for this. On $Z^{+}$,define $*$ by $a * b = a$.

Consider a binary operation $*$ on $N$ defined as $a * b = a^{3} + b^{3}$. Choose the correct answer.

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

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Show that $: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ defined by $a b = a + 2b$ is not commutative.

Determine whether or not each of the definitions of $$ given below gives a binary operation. In the event that $$ is not a binary operation,give justification for this. On $Z^{+}$,define $$ by $a b = a$.

Consider a binary operation $$ on $N$ defined as $a b = a^{3} + b^{3}$. Choose the correct answer.

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