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Question Number 93933 by oustmuchiya@gmail.com last updated on 16/May/20

$$Let{\ast }^{\prime }bethebinaryoperationontheset\{1,2,3,4,5\}definedby\mathrm{a}{\ast }^{\prime }\mathrm{b}=\mathrm{H}.\mathrm{C}.\mathrm{F}ofaandb.$$$$Istheoperation{\ast }^{\prime }sameastheoperation\ast definedabove?justifyyouranswer.$$

Commented by Rasheed.Sindhi last updated on 16/May/20

$$Operation{\ast }^{\prime }isdefinedinthe$$$$question.Whatdoyoumeanby$$$$‘‘operation{\ast }^{″}?$$

Commented by oustmuchiya@gmail.com last updated on 16/May/20

$$Thatishowthequestionis.Idesperatelyjustneedhelp.$$

Commented by mr W last updated on 16/May/20

$$onecannotgivearightanswerto$$$$awrongquestion!$$

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

$$Actuallyitisanassignment.The$$$$questionsareasfollows:$$$$1.Let{\ast }^{\prime }bethebinaryoperationon$$$$theset\{1,2,3,4,5\}definedby\mathbf{a}{\ast }^{\prime }\mathbf{b}=\mathrm{H}.\mathrm{C}.\mathrm{F}.$$$$of\mathbf{a}and\mathbf{b}.Istheoperation{\ast }^{\prime }same$$$$astheoperation\ast definedabove.$$$$justifyyouranswer.$$$$2.Let\ast bethebinaryoperationon$$$$\mathrm{N}givenby\mathbf{a}\ast \mathbf{b}=\mathrm{L}.\mathrm{C}.\mathrm{M}.of\mathbf{a}\mathrm{and}\mathbf{b}.$$$$\mathrm{F}ind\left(\mathbf{i}\right)5\ast 7,20\ast 16$$$$\left(\mathbf{ii}\right)is\ast communitative?$$$$\left(\mathbf{iii}\right)is\ast associative?$$$$\left(\mathbf{iv}\right)findtheidentityof\ast in\mathbf{N}$$$$\left(\mathbf{v}\right)whichelementsof\mathbf{N}are$$$$invertiblefortheoperation\ast ?$$$$$$

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