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Question Number 104692 by 175mohamed last updated on 23/Jul/20

Answered by OlafThorendsen last updated on 23/Jul/20

Car∪Bus = Car⊕Bus−Car∩Bus Car∪Bus = 20+50−10 = 60% and Car∪Bus−Car∩Bus = 60−10 = 50% Car = 20% Bus = 50% AND(Car,Bus) = 10% OR(Car,Bus) = 60% XOR(Car,Bus) = 50%

$$\mathrm{Car}\cup\mathrm{Bus}\:=\:\mathrm{Car}\oplus\mathrm{Bus}−\mathrm{Car}\cap\mathrm{Bus} \\ $$$$\mathrm{Car}\cup\mathrm{Bus}\:=\:\mathrm{20}+\mathrm{50}−\mathrm{10}\:=\:\mathrm{60\%} \\ $$$$\mathrm{and}\:\mathrm{Car}\cup\mathrm{Bus}−\mathrm{Car}\cap\mathrm{Bus}\:=\:\mathrm{60}−\mathrm{10}\:=\:\mathrm{50\%} \\ $$$$\mathrm{Car}\:=\:\mathrm{20\%} \\ $$$$\mathrm{Bus}\:=\:\mathrm{50\%} \\ $$$$\mathrm{AND}\left(\mathrm{Car},\mathrm{Bus}\right)\:=\:\mathrm{10\%} \\ $$$$\mathrm{OR}\left(\mathrm{Car},\mathrm{Bus}\right)\:=\:\mathrm{60\%} \\ $$$$\mathrm{XOR}\left(\mathrm{Car},\mathrm{Bus}\right)\:=\:\mathrm{50\%} \\ $$

Answered by 1549442205PVT last updated on 23/Jul/20

Denote A−set of the persons travel by car,B−by bus⇒A∩B− set of persons travel by both means (car and bus) From the hypothesis we have m(A)=20%,m(B)=50%,m(A∩B)=10% Since m(A∩B)=m(A)+m(B)−m(A∪B) ,so m(A∪B)=m(A)+m(B)−m(A∩B) =20%+50%−10%=60%

$$\mathrm{Denote}\:\mathrm{A}−\mathrm{set}\:\mathrm{of}\:\mathrm{the}\:\mathrm{persons}\:\mathrm{travel} \\ $$$$\mathrm{by}\:\mathrm{car},\mathrm{B}−\mathrm{by}\:\mathrm{bus}\Rightarrow\mathrm{A}\cap\mathrm{B}−\:\mathrm{set}\:\mathrm{of}\:\mathrm{persons}\: \\ $$$$\mathrm{travel}\:\mathrm{by}\:\mathrm{both}\:\mathrm{means}\:\left(\mathrm{car}\:\mathrm{and}\:\mathrm{bus}\right) \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{hypothesis}\:\mathrm{we}\:\mathrm{have} \\ $$$$\mathrm{m}\left(\mathrm{A}\right)=\mathrm{20\%},\mathrm{m}\left(\mathrm{B}\right)=\mathrm{50\%},\mathrm{m}\left(\mathrm{A}\cap\mathrm{B}\right)=\mathrm{10\%} \\ $$$$\mathrm{Since}\:\mathrm{m}\left(\mathrm{A}\cap\mathrm{B}\right)=\mathrm{m}\left(\mathrm{A}\right)+\mathrm{m}\left(\mathrm{B}\right)−\mathrm{m}\left(\mathrm{A}\cup\mathrm{B}\right) \\ $$$$,\mathrm{so}\:\mathrm{m}\left(\mathrm{A}\cup\mathrm{B}\right)=\mathrm{m}\left(\mathrm{A}\right)+\mathrm{m}\left(\mathrm{B}\right)−\mathrm{m}\left(\mathrm{A}\cap\mathrm{B}\right) \\ $$$$=\mathrm{20\%}+\mathrm{50\%}−\mathrm{10\%}=\mathrm{60\%} \\ $$

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