For-any-integer-n-let-I-n-be-the-interval-n-n-1-Define-R-x-y-R-both-x-y-I-n-for-some-n-Z-Then-R-is-A-reflexive-on-R-B-symmetric-C-transitive-D-an-equivalence-relation-

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Question Number 119757 by Ar Brandon last updated on 26/Oct/20

$$\mathrm{For}\mathrm{any}\mathrm{integer}n,\mathrm{let}{I}_n\mathrm{be}\mathrm{the}\mathrm{interval}(n,n+1).$$$$\mathrm{Define}$$$$\mathcal{R}=\{(\mathrm{x},\mathrm{y})\in \mathbb{R}\mid \mathrm{both}\mathrm{x},\mathrm{y}\in I_n\mathrm{for}\mathrm{some}n\in \mathbb{Z}\}$$$$\mathrm{Then}\mathcal{R}\mathrm{is}$$$$\left(\mathrm{A}\right)\mathrm{reflexive}\mathrm{on}\mathbb{R}$$$$\left(\mathrm{B}\right)\mathrm{symmetric}$$$$\left(\mathrm{C}\right)\mathrm{transitive}$$$$\left(\mathrm{D}\right)\mathrm{an}\mathrm{equivalence}\mathrm{relation}$$

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