1: Let A be a non-empty set. Which of the properties reflexive, irreflexive, symmetric, asymmet- ric, antisymmetric, transitive and total do the following binary relations on A have: (a) ∅ (no two elements form A are related to each other) (b) {(a, b) : a, b ∈ A, a != b} (every two different elements from A are related to each other) (c) {(a, a) : a ∈ A} (each element is related to itself and is not related to any other element)

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A: We can solve this as follows:

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A: Definitions:

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