Henri P.

# Let E be a non-empty set. Let's consider the inclusion relation over P(E): (∀x, y ∈ P(E))(X ≤ Y ⇔ X ⊂ Y )

Let E be a non-empty set. Let's consider the inclusion relation over P(E): (∀x, y ∈ P(E))(X ≤ Y ⇔ X ⊂ Y )

(a) Show that it is an order relation.

(b) Show that it is total if, and only if, E = {a}

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I know that I have to prove that it is reflexive, antisymmetric and transitive, but how do I do that? And how do I show that it is total when E = {a}?