1. Give an example of a strict partial order on Z≥1 such that every integer has exactly two different immediate successors. 2. Prove that for a partial order  on A when A is finite there must be an a...

1. Give an example of a strict partial order on Z≥1 such that every integer has exactly two different immediate successors.

2. Prove that for a partial order  on A when A is finite there must be an a ∈ A that has fewer than two immediate successors.