Identify the correct steps involved in showing that lexicographic order is transitive. (Check all that apply.) Check All That Apply Let (a, b) (c,d) (e, f. If one of the given inequalities is an equality, we will have two cases: a = b < cand a < b = c, then, there is nothing to prove. Hence, we may assume that (a, b) (c,d) < (e, f. If one of the given inequalities is an equality, we have a = b = c; then, there is nothing to prove. Hence, we may assume that (a, b) (c,d) (e. f). If a e, then by the transitivity of the underlying relation, we know that ac, and so, (a, b) (e. f. If a c, then by the transitivity of the underlying relation, we know that a e, and so, (a, b) (e. f). If ce, then by the transitivity of the underlying relation, we know that a e, and so, (a, b) (e, f.
Identify the correct steps involved in showing that lexicographic order is transitive. (Check all that apply.) Check All That Apply Let (a, b) (c,d) (e, f. If one of the given inequalities is an equality, we will have two cases: a = b < cand a < b = c, then, there is nothing to prove. Hence, we may assume that (a, b) (c,d) < (e, f. If one of the given inequalities is an equality, we have a = b = c; then, there is nothing to prove. Hence, we may assume that (a, b) (c,d) (e. f). If a e, then by the transitivity of the underlying relation, we know that ac, and so, (a, b) (e. f. If a c, then by the transitivity of the underlying relation, we know that a e, and so, (a, b) (e. f). If ce, then by the transitivity of the underlying relation, we know that a e, and so, (a, b) (e, f.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the Cartesian product of two posets under the lexicographic ordering relation.
Identify the correct steps involved in showing that lexicographic order is transitive. (Check all that apply.)
Check All That Apply
Let (a, b) (c,d) = (e, fj.
If one of the given inequalities is an equality, we will have two cases: a = b < cand a < b = c, then, there is nothing to prove. Hence, we may assume that (a, b) < (c,d) < (e, fi.
If one of the given inequalities is an equality, we have a = b = c; then, there is nothing to prove. Hence, we may assume that (a, b) ≤ (c,d) < (e, f).
If a < e, then by the transitivity of the underlying relation, we know that a c, and so, (a, b) ≤ (e, f).
If a < c, then by the transitivity of the underlying relation, we know that a e, and so, (a, b) < (e, f).
If c< e, then by the transitivity of the underlying relation, we know that a e, and so, (a, b) < (e, f.
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