When set A is a separate domain, the definition is
(1) If there is x (
(2) If there is X (
(3) If any x any y (
(4) If any x any y (
In this way, it looks simple.
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1, when judging reflexivity and reflexivity, you only look at everything.
2. the relation r on set a is a subset of cartesian product a× a. as long as < x, y > ensures that x, y∈A is enough, x and y don't have to take all the elements in a.
The range in the definition of symmetry and antisymmetry is a hint. For example, in the definition of symmetry, the antecedent of implication is X, Y ∈ A ∧.
So is antisymmetry. Find out from R.