5 marks 3. Consider the set T whose elements are all the factors of 1000 and denote a relation 1' C T x T such that orb if a is a factor of b. i. Verify that (T,1') is a poset. ii. Give the least upper bound for 8 and 25, as well as one other upper bound ( 1). iv. Is (T,1') a lattice? Explain why/why not. 5 marks 4. Let p be a relation on Z'l' such that opb if there exists an n E Z such that a x 5\" = b. i. Give any 3 ordered pairs of the relation such that a, b > 1. ii. Determine whether or not any of (5, 20), (25, 1), (7, 7) are elements of p. iii. Determine whether or not the relation is symmetric, transitive, antisymmetric or reexive, and state whether it is an equivalence relation, poset, or neither. Make any further relevant observations depending on the outcome. 5 marks