Need help with 1 0.Determine whether Ris an equivalence relation, a partial ordering, or neither.3. Let A = {armadillo, bear, erocodile,dolphin, eagle, fox}. Construct a par-tial ordering3 on A...

Need help with 1

Extracted text: 1. Let R and S be equivalence relations on a set A; recall that by definition R,SCAX A. Prove that RAS is an equivalence relation. 2. Define the relation Ron Z as follows: for r, y EZ, xRy if and only y –x > 0. Determine whether Ris an equivalence relation, a partial ordering, or neither. 3. Let A = {armadillo, bear, erocodile,dolphin, eagle, fox}. Construct a par- tial ordering3 on A that satisfies the conditions below. (You may draw a Hasse diagram to demonstrate your partial ordering. armadillo 3 eagle. The least upper bound of the set {bear, eagle, fox} is "crocodile". "fox" is a minimal element of the partial ordering. 4. Given the slightly blurry Hasse diagram below, find all maximal, minimal,