Let A be a non-empty set, ≃ ⊆ A × A an equivalence realtionship and ⪯ ⊆ A × A a partial order, both over A. Consider the quotient set: A / ≃, and define the following relation ≪ ⊆ (A/ ≃) × (A/ ≃) where (S1, S2) ∈ ≪ if, and only if, there is an a ∈ S1 such that for all b ∈ S2, a ⪯ b. 1.) How to show that ≪r is is a partial order over A/ ≃ where ≪r is the reflex cause of ≪. 2.) Is it true that A has a minimal element according to ⪯ if, and only if, A/ ≃ has a minimal element according to ≪r ? How to show if it is true or false (in such case suggest a counterexample)

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