Example of an Equivalence Relation
lConsider the relation
Òis a homophone ofÓ
(Òsounds the same asÓ) on a set of words, such as {ÒairÓ, ÒereÓ, ÒheirÓ, ÒbuyÓ, ÒbyÓ, ÒbyeÓ, ÒdewÓ, ÒdoÓ, ÒdueÓ, ÒeweÓ, ÒyouÓ, ÒyewÓ}
(Òsounds the same asÓ) on a set of words, such as {ÒairÓ, ÒereÓ, ÒheirÓ, ÒbuyÓ, ÒbyÓ, ÒbyeÓ, ÒdewÓ, ÒdoÓ, ÒdueÓ, ÒeweÓ, ÒyouÓ, ÒyewÓ}
lReflexive: Every x is a homophone of
x.
lSymmetric: If x is a homophone of y then y is a homophone of x.
lTransitive: If x is a homophone of y
and y is a homophone of z, then x is a homophone of z.
lTherefore this is an
equivalence relation.