Let S denote the set of all five sequences on Z. Consider the set T of ten elements of S:

S₁ = (4, 2, 9, 5, 5) S₂ = (4, 2, 3, 1, 2) S₃ = (-2, 3, 3, -2, 4)

S₄ = (7, 6, 8, 3, 9) S₅ = (0, -1, 5, 1, 3) S₆ = (3, 1, 3, 0, 3)

S₇ = (4, 2, 4, 5, 5) S₈ = (4, -2, 9, 1, 6) S₉ = (4, 2, 9, -1, 6)

S₁₀ = (4, 2, 9, 5, 6) (a) Sort the ten elements of T into lexicographic order, smallest to largest. (b) Using the relation is dominated by on S: 1. Find an element of S which is dominated by all of these ten. 2. Find two elements in the ten which are not comparable under this relation.