Let A be a set with a partial order R. For each a∈A, let Sa = {x∈A: xRa}. Let F={Sa: a∈A}. Then F is a subset of P (A) and thus may be partially ordered by ⊆, inclusion. a) Show that if aRb, then Sa ⊆ Sb. b) Show that if Sa ⊆ Sa, then aRb.
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