Question Number 93933 by oustmuchiya@gmail.com last updated on 16/May/20
$${Let}\:\ast'\:{be}\:{the}\:{binary}\:{operation}\:{on}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\}\:{defined}\:{by}\:\mathrm{a}\ast'\mathrm{b}=\mathrm{H}.\mathrm{C}.\mathrm{F}{of}\:{a}\:{and}\:{b}.\: \\ $$$${Is}\:{the}\:{operation}\:\ast'\:{same}\:{as}\:{the}\:{operation}\:\ast\:{defined}\:{above}?\:{justify}\:{your}\:{answer}. \\ $$
Commented by Rasheed.Sindhi last updated on 16/May/20
$${Operation}\:\ast'\:{is}\:{defined}\:{in}\:{the} \\ $$$${question}.{What}\:{do}\:{you}\:{mean}\:{by} \\ $$$$``{operation}\:\ast''? \\ $$
Commented by oustmuchiya@gmail.com last updated on 16/May/20
$${That}\:{is}\:{how}\:{the}\:{question}\:{is}.\:{I}\:{desperately}\:{just}\:{need}\:{help}. \\ $$
Commented by mr W last updated on 16/May/20
$${one}\:{can}\:{not}\:{give}\:{a}\:{right}\:{answer}\:{to}\: \\ $$$${a}\:{wrong}\:{question}! \\ $$
Commented by prakash jain last updated on 16/May/20
hi oustmuchiya check your textbook maybe this question is part of a group of question and '*' is defined before this question
Commented by oustmuchiya@gmail.com last updated on 16/May/20
$${Actually}\:{it}\:{is}\:{an}\:{assignment}.\:{The} \\ $$$${questions}\:{are}\:{as}\:{follows}: \\ $$$$\mathrm{1}.\:{Let}\:\ast'\:{be}\:{the}\:{binary}\:{operation}\:{on}\: \\ $$$${the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\}\:{defined}\:{by}\:\boldsymbol{\mathrm{a}}\ast'\boldsymbol{\mathrm{b}}=\mathrm{H}.\mathrm{C}.\mathrm{F}. \\ $$$${of}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}.\:{Is}\:{the}\:{operation}\:\ast'\:{same} \\ $$$${as}\:{the}\:{operation}\:\ast\:{defined}\:{above}. \\ $$$${justify}\:{your}\:{answer}. \\ $$$$\mathrm{2}.\:{Let}\:\ast\:{be}\:{the}\:{binary}\:{operation}\:{on} \\ $$$$\mathrm{N}\:{given}\:{by}\:\boldsymbol{\mathrm{a}}\ast\boldsymbol{\mathrm{b}}=\mathrm{L}.\mathrm{C}.\mathrm{M}.\:{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}. \\ $$$$\mathrm{F}{ind}\:\:\left(\boldsymbol{\mathrm{i}}\right)\:\mathrm{5}\ast\mathrm{7},\:\:\mathrm{20}\ast\mathrm{16}\:\: \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\:{is}\:\ast\:{communitative}? \\ $$$$\left(\boldsymbol{\mathrm{iii}}\right)\:{is}\:\ast\:{associative}? \\ $$$$\left(\boldsymbol{\mathrm{iv}}\right)\:{find}\:{the}\:{identity}\:{of}\:\ast\:{in}\:\boldsymbol{\mathrm{N}} \\ $$$$\left(\boldsymbol{\mathrm{v}}\right)\:{which}\:{elements}\:{of}\:\boldsymbol{\mathrm{N}}\:{are} \\ $$$$\:\:\:\:\:\:\:\:{invertible}\:{for}\:{the}\:{operation}\:\ast? \\ $$$$\:\: \\ $$