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}
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.