1. Let be a partial order on a set A. Prove that there is at most one minimum element in A under . (That is, prove that if a ∈ A and b ∈ A are both minimum elements, 2. Let be a partial order on a...

1. Let be a partial order on a set A. Prove that there is at most one minimum element in A under . (That is, prove that if a ∈ A and b ∈ A are both minimum elements,

2. Let be a partial order on a set A, and let a ∈ A be a minimum element under . Prove that a is also a minimal element.