Question

State whether 14/(-5) is closed under division for z

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

G is said to be closed under the operation *

$\sf{If \: for \: \: a, b \: \in G \: \: \: we \: have \: \: a*b \in G}$

TO CHECK

$\sf{ Whether \: \: \mathbb{ Z }\: \: is \: closed \: under \: division\: }$

CALCULATION

$\sf{Here \: \mathbb{Z} \: \: is \: the \: set \: of \: integers }$

$\sf{\mathbb{Z} = \{ 0, \pm1, \pm2, \pm3,...... \} }$

$\sf{Now \: - 5, 14 \in \mathbb{Z} \: \: but \: \: 14/(-5)=-2.8 \notin \mathbb{Z} \: \: }$

$\sf{ \therefore \: \: \mathbb{ Z }\: \: is \: not \: closed \: under \: division\: }$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Show that the set Q+ of all positive rational numbers forms an abelian group under the operation * defined by a*b= 1/2(ab)

https://brainly.in/question/21467351