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Question Number 157887 by Tawa11 last updated on 29/Oct/21

Commented by Tawa11 last updated on 29/Oct/21

$$\mathrm{Proof}\mathrm{please}$$

Commented by Rasheed.Sindhi last updated on 29/Oct/21

$$fisnotafunction.{It}^{\prime }sarelation.$$$$Becausef\left(3\right)isnotunique.$$

Answered by Rasheed.Sindhi last updated on 29/Oct/21

$$f=\{(\beta ,a),(3,b),(3,c)\}$$$$f\left(\beta \right)=a,f\left(3\right)=b,f\left(3\right)=c$$$$g=\{(a,3),(b,\beta ),(c,\beta )\}$$$$g\left(f\left(\beta \right)\right)=g\left(a\right)=3$$$$g\left(f\left(3\right)\right)=g\left(b\right)=\beta$$$$g\left(f\left(3\right)\right)=g\left(c\right)=\beta$$$$gof=\{(\beta ,3),(3,\beta )\}$$$$g=\{(a,3),(b,\beta ),(c,\beta )\}$$$$g\left(a\right)=3,g\left(b\right)=\beta ,g\left(c\right)=\beta$$$$f=\{(\beta ,a),(3,b),(3,c)\}$$$$f\left(g\left(a\right)\right)=f\left(3\right)=b,c$$$$f\left(g\left(b\right)\right)=f\left(\beta \right)=a$$$$f\left(g\left(c\right)\right)=f\left(\beta \right)=a$$$$fog=\{(a,b)(a,c)(b,a),(c,a)\}$$

Commented by Tawa11 last updated on 29/Oct/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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