# Discribe types of Equivalence relations? Describe only transtive, symmetric, anti-symmetric, and reflexive properties with examples.Reflexive Symmetric Anti-symmetric Transtive

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sciencesolve | Certified Educator

You may consider the relations of equality `=` as a equivalence relation over the set of integer numbers Z.

Notice that the equality is **reflexive** because for any `x in Z` , `x=x` holds.

The equality relation is also **symmetric** because `x=y` implies `y=x` .

The equality relation is **transitive** since if `x=y` and `y=z` yields `x = z` .

**Hence, the relation of equality is an equivalence relation over `Z` .**