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

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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?

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