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let the relation [tex]\propto[/tex] on a set S have the properties

(i) a [tex]\propto[/tex] a for every a [tex]\in[/tex] S

(II) if a [tex]\propto[/tex] b and b [tex]\propto[/tex] c then c [tex]\propto[/tex] a

show that [tex]\propto[/tex] is an equivalence relation on S.

Does every equivalence relation on S satisfy (i) and (ii)

I'm not sure where to start this i know

(i) is the reflexive property and (ii) is the Transitive property.

Im not sure where to go or how to tackle this,some pointers would be greatly appreciated

(i) a [tex]\propto[/tex] a for every a [tex]\in[/tex] S

(II) if a [tex]\propto[/tex] b and b [tex]\propto[/tex] c then c [tex]\propto[/tex] a

show that [tex]\propto[/tex] is an equivalence relation on S.

Does every equivalence relation on S satisfy (i) and (ii)

I'm not sure where to start this i know

(i) is the reflexive property and (ii) is the Transitive property.

Im not sure where to go or how to tackle this,some pointers would be greatly appreciated

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