(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Deciede if the following are equivalence relations on Z. If so desribe the eqivalence classes

i) a[itex]\equiv[/itex] b if [itex]\left|a\right|[/itex] = [itex]\left|b\right|[/itex]

ii) a[itex]\equiv[/itex] b if b=a-2

2. Relevant equations

3. The attempt at a solution

i) [itex]\left|a\right|[/itex] = [itex]\left|a\right|[/itex] so its reflexive

[itex]\left|a\right|[/itex] = [itex]\left|b\right|[/itex] is equivalent to [itex]\left|b\right|[/itex] = [itex]\left|a\right|[/itex] so its symmetric

[itex]\left|a\right|[/itex] = [itex]\left|b\right|[/itex] and [itex]\left|b\right|[/itex] = [itex]\left|c\right|[/itex] then [itex]\left|a\right|[/itex] = [itex]\left|c\right|[/itex] for all values a,b and c elemets of Z so its transitive.

Are there infinite equivalence classes??

ii) a=a so its reflexive

b=a-2 [itex]\neq[/itex] a=b-2 so its not symetric, am i right in thinking this?

Thanks for reading

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Equivalence Relations

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