Show whether Reflexive, Symmetric, & Anti-symmetric to show whether the followin

Question

Show whether Reflexive, Symmetric, & Anti-symmetric to show whether the following is an equivalence relation:

Explanation / Answer

aRb < = > 2| b-a 1) Reflexive : 2 | 0 2| a - a aRa 2) Symmetric 2|b-a b-a = 2d a-b = -2d 2|a-b bRa 3) Anti symmetric aRb 2| b-a and bRc 2| a-b, does not necessarily imply a=b for example take b=2 and a = 0. 4) Transitive aRb 2|b-a then b-a = 2g and bRc < => 2|c-b then c-b = 2f, so b-a + c-b = c-a = 2g + 2f = 2(g+f) 2|c-a aRc It is a equivalence relation because it is reflexive, symmteric and transitive. But it is not anti-symmetric.

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