Chapter 9.6, Problem 44E

To determine

(a)

Whether the poset $\text{({1, 3, 6, 9, 12}, |}\text{)}$ is alattice or not.

To determine

(b)

Whether the poset $\text{({1, 5, 25, 125}, |)}$ is a lattice or not.

To determine

(c)

Whether the poset $\text{(Z,}\ge \text{)}$ is a lattice or not.

To determine

(d)

Whether the poset $\text{(P(S),}\supseteq ),where\text{P(S)}$ is the power set of $S$ is a lattice or not.