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Example

• p(x, y) : <=> x+y is even

  Equivalence relation on N.

• r(x, y) : <=> x₀+y₁ = x₁+y₀

  Equivalence relation on R x R.

• s(x, y) : <=> x is parallel to (or coincides with) y

  Equivalence relation on the set of all lines in the plane.

• t(x, y) : <=> x has the same age as y

  Equivalence relation on the set of all people.