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Unit 1 · Discrete Structures and Optimization Paper 2 CS · September 2022

Let ε = 0.0005 and let Rε = {(x, y) ∈ ℝ2 : |x − y| < ε}, which can be interpreted as 'approximately equal'. Rε is
(A) Reflexive
(B) Symmetric
(C) Transitive
Choose the correct answer from the options given below:

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. (A) and (B) only true

Explanation

|x − x| = 0 < ε and |x − y| = |y − x|, so it is reflexive and symmetric. It is not transitive: 0 ~ 0.0003 and 0.0003 ~ 0.0006, but |0 − 0.0006| > ε.

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