5 votes 5 votes A binary relation $R ⊆ (S ×S)$ is said to be Euclidean if for every $a, b, c ∈ S, (a, b) ∈ R$ and $(a, c) ∈ R$ implies $(b, c) ∈ R$. Which of the following statements is valid? If $R$ is Euclidean, $(b, a) ∈ R$ and $(c, a) ∈ R$, then $(b, c) ∈ R$, for every $a, b, c ∈ S$ If $R$ is reflexive and Euclidean, $(a, b) ∈ R$ implies $(b, a) ∈ R$, for every $a, b ∈ S$ If $R$ is Euclidean, $(a, b) ∈ R$ and $(b, c) ∈ R$, then $(a, c) ∈ R$, for every $a, b, c ∈ S$ None of the above. Set Theory & Algebra cmi2015 relations set-theory&algebra + – Mk Utkarsh asked May 12, 2018 Mk Utkarsh 1.1k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments mrinmoyh commented Sep 30, 2018 reply Follow Share what is Euclidian? 1 votes 1 votes Kritika14 commented Jul 4, 2019 reply Follow Share Why option C is not true? Isn't it the same statement in the question? 0 votes 0 votes Kushagra Chatterjee commented Jul 5, 2019 reply Follow Share No they are not the same. 1 votes 1 votes Please log in or register to add a comment.
Best answer 6 votes 6 votes Lets see option $B$ If $R$ is reflexive then $(a,a)$ belongs to $R$ It is given that $(a,b)$ belongs to $R$ So, $(a,b) ∈ R$ and $(a,a)$ ∈ $R$ that implies $(b,a) ∈ R$ for all $a,b ∈ S$ [ since $R$ is euclidean] Thus option $B$ is the correct answer. Kushagra Chatterjee answered May 12, 2018 • edited Jun 8, 2018 by Milicevic3306 Kushagra Chatterjee comment Share Follow See all 3 Comments See all 3 3 Comments reply Kritika14 commented Jul 4, 2019 reply Follow Share Why you have checked only option B, what about option A and C? 0 votes 0 votes srestha commented Jul 5, 2019 reply Follow Share It is a special property, which called as Euclidean. C) is telling about transitivity property. But transitivity property is not Euclidean Similarly A) also not a valid Euclidean 1 votes 1 votes Kritika14 commented Jul 5, 2019 reply Follow Share Yeah, got it! Thank you 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Answer: soujanyareddy13 answered May 6, 2021 soujanyareddy13 comment Share Follow See all 0 reply Please log in or register to add a comment.