Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 34063 by rahul 19 last updated on 30/Apr/18

$$\mathbf{L}\mathrm{et}\mathrm{A}=\{1,2,3,4\}.\mathrm{N}umber\mathrm{of}\mathrm{functions}$$$$\mathrm{f}:\mathrm{A}\to A\mathrm{satisfying}\mathrm{f}\left(\mathrm{f}\left(x\right)\right)=x\mathrm{\forall }x\in \mathrm{A},\mathrm{is}?$$

Commented by rahul 19 last updated on 30/Apr/18

$$Ans.is13....$$

Commented by rahul 19 last updated on 30/Apr/18

$$doesthisgives13?$$

Commented by Rasheed.Sindhi last updated on 30/Apr/18

$$\mathrm{For}\mathrm{example}:$$$$\{(1,2),(2,1),(3,4),(4,3)\}$$$$\mathrm{f}\left(1\right)=2,\mathrm{f}\left(\mathrm{f}\left(1\right)\right)=\mathrm{f}\left(2\right)=1$$$$\mathrm{f}\left(\mathrm{f}\left(2\right)\right)=\mathrm{f}\left(1\right)=2$$$$$$$$a,b,c,d\in \mathrm{A},a,b,c,d\mathrm{are}\mathrm{different}$$$$\{(a,a),(b,b),(c,c),(d,d)\}$$$$\{(a,a),(b,b),(c,d),(d,c)\}$$$$\{(a,b),(b,a),(c,d),(d,c)\}$$$$$$$$\mathrm{Continue}$$

Answered by Rasheed.Sindhi last updated on 30/Apr/18

$$\mathrm{Domain}\left(\mathrm{f}\right)=\mathrm{A},\mathrm{the}\mathrm{function}\mathrm{have}4\mathrm{orderd}$$$$\mathrm{pairs},\mathrm{the}\mathrm{pair}\mathrm{of}\mathrm{f}\mathrm{is}\mathrm{either}\mathrm{of}(a,a)\mathrm{type}$$$$\mathrm{or}\mathrm{if}\mathrm{it}\mathrm{is}(a,b)\mathrm{with}a\ne \mathrm{b}\mathrm{then}\mathrm{the}\mathrm{f}\mathrm{also}$$$$\mathrm{contains}(b,a)\mathrm{because}\mathrm{of}\mathrm{the}\mathrm{condition}$$$$\mathrm{f}\left(\mathrm{f}\left(x\right)\right)=x\mathrm{\forall }x\in \mathrm{A}.$$$$\mathrm{The}\mathrm{ordered}\mathrm{pair}\mathrm{containing}1\mathrm{as}\mathrm{abscissa}$$$$\mathrm{may}\mathrm{be}(1,1),(1,2),(1,3),(1,4)$$$$(1,1):(2,2),(2,3),(2,4)[(2,1)\mathrm{is}\mathrm{impossible}$$$$------$$$$(1,1),(2,2),(3,3),(4,4)$$$$(1,1),(2,2),(3,4),(4,3)$$$$(1,1),(2,3),(3,2),(4,4)$$$$(1,1),(2,4),(3,3),(4,2)$$$$-----$$$$(1,2),(2,1),(3,4),(4,3)$$$$(1,2),(2,1),(3,3),(4,4)$$$$(1,3),(2,4),(3,1),(4,2)$$$$(1,3),(2,2),(3,1),(4,4)$$$$(1,4)(2,3)(3,2),(4,1)$$$$(1,4)(2,2)(3,3),(4,1)$$$$$$

Commented by Rasheed.Sindhi last updated on 30/Apr/18

$$\mathrm{I}\mathrm{think}\mathrm{the}\mathrm{answer}\mathrm{should}\mathrm{be}10.$$

Commented by rahul 19 last updated on 30/Apr/18

$$\mathcal{T}hank\mathcal{Y}ou\mathcal{S}ir!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com