On the set of all natural numbers N,which one | vedclass

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

Question

(C) binary operation $*$ on a set $N$ is a function $*: N 	imes N 	o N$. This means for any $a, b \in N$,the result $a * b$ must also be in $N$.$(A)

Vedclass · Accepted Answer

$a * b = a + 3b$

Vedclass · Answer

(C) binary operation $*$ on a set $N$ is a function $*: N 	imes N 	o N$. This means for any $a, b \in N$,the result $a * b$ must also be in $N$.$(A)$ $a * b = \sqrt{ab}$: If $a=1, b=2$,then $a * b = \sqrt{2} 
otin N$.$(B)$ $a * b = \frac{a-b}{a+b}$: If $a=1, b=2$,then $a * b = \frac{-1}{3} 
otin N$.$(C)$ $a * b = a + 3b$: Since $a, b \in N$,$a + 3b$ is always a natural number. Thus,this is a binary operation.$(D)$ $a * b = 3a - 4b$: If $a=1, b=2$,then $a * b = 3(1) - 4(2) = -5 
otin N$.Hence,option $C$ is correct.

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

On the set of all natural numbers $N$,which one of the following $*$ is a binary operation?

Similar Questions

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a \,^\, b = a b^{2}$. Determine whether the operation is commutative and associative.

State whether the following statement is true or false and justify your answer: If $^$ is a commutative binary operation on $N$,then $a ^ (b ^* c) = (c ^* b) ^* a$.

Is $^$ defined on the set $\{1, 2, 3, 4, 5\}$ by $a \,^\, b = \text{L.C.M. of } a \text{ and } b$ a binary operation? Justify your answer.

Let $^{\prime}$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a ^{\prime} b = \text{H.C.F. of } a \text{ and } b$. Is the operation $^{\prime}$ same as the operation $$ defined in Exercise $4$ above? Justify your answer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

On the set of all natural numbers $N$,which one of the following $*$ is a binary operation?

Similar Questions

Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a \,^*\, b = a b^{2}$. Determine whether the operation is commutative and associative.

State whether the following statement is true or false and justify your answer: If $^*$ is a commutative binary operation on $N$,then $a ^* (b ^* c) = (c ^* b) ^* a$.

Is $^*$ defined on the set $\{1, 2, 3, 4, 5\}$ by $a \,^*\, b = \text{L.C.M. of } a \text{ and } b$ a binary operation? Justify your answer.

Let $*^{\prime}$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a *^{\prime} b = \text{H.C.F. of } a \text{ and } b$. Is the operation $*^{\prime}$ same as the operation $*$ defined in Exercise $4$ above? Justify your answer.