1 votes 1 votes Consider the equivalence relation R = $\{(x,y) \, | \, x-y \,is\,an\,integer\}$ (b) What is the equivalence class of 1/2 for this equivalence relation? Set Theory & Algebra kenneth-rosen discrete-mathematics set-theory&algebra relations + – Ayush Upadhyaya asked Jun 30, 2018 • edited Mar 4, 2019 by Pooja Khatri Ayush Upadhyaya 576 views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Soumya29 commented Jun 30, 2018 reply Follow Share $\{...-2.5,-1.5,.5, 1.5........\}?$ 0 votes 0 votes Ayush Upadhyaya commented Jun 30, 2018 reply Follow Share Seems to be correct because answer given is $\{n+\frac{1}{2}.n \, | \, n \in Z\}$ but how can it contain some fractional elements because the relation is on Z? 0 votes 0 votes Soumya29 commented Jun 30, 2018 reply Follow Share How relation is on $Z$ ? It must be on $R$ because equivalence class of $\frac{1}{2}$ is asked. 0 votes 0 votes Soumya29 commented Jul 1, 2018 reply Follow Share @Ayush, Given answer is $\{n+\frac{1}{2}.n|n∈Z\} \ or \ \{n+\frac{1}{2}|n∈Z\}?$ 0 votes 0 votes Ayush Upadhyaya commented Jul 1, 2018 reply Follow Share Sorry soumya, it was a typo. Answer is the latter expression in your comment above 0 votes 0 votes Ayush Upadhyaya commented Jul 1, 2018 reply Follow Share So for this to be possible, does this relation R needs to be necessarily defined on real numbers and not integers? 0 votes 0 votes Soumya29 commented Jul 1, 2018 reply Follow Share Yes. Otherwise, if it were defined on $Z$ then it would be empty. 1 votes 1 votes Please log in or register to add a comment.