Let A = {a, b, c, d) and let P(A) be the power set of A. a. List all the members (subsets of A) in P(A). b. Define a relation R on A by x Ry if x y. Show that P(A) is a poset under R.

Let A = {1, 2, 3, 4). Define the relation R on A by x R y if x ≤ y. a. List all the members of R b. Determine if R is reflexive, symmetric, anti-symmetric, transitive.

Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not transitive.

Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c), (c, d), (d, d)} be arelation on A. Which of the properties reflexive, symmetric and transitive does the relation R possess? If Rdoes not possess one of these properties, explain why. How do I know where to stop? How do I know when I have proven transitivity? for example? I have difficulties with knowing if my prove is complete or not