lConsider the relation Òis a synonym forÓ
(Òmeans the same asÓ)
lReflexive:
Every x is a synomym for x.
lSymmetric: If
x is a synomym of y then y is a synomym of x.
lTransitive:
NOT: If x is a synomym of y and y is a synomym of z, then x is a synomym of z.
(Example: ÒangryÓ is a synonym for ÒmadÓ, and ÒmadÓ is a synonym for ÒinsaneÓ, but ÒangryÓ is not a synonym for ÒinsaneÓ.)
lTherefore this is a not an equivalence relation.