Let A be the set of all binary strings of length 3. Let ≼be a relation on A such that for any s ∈A and t ∈A, s ≼t if and only if the positive integer with binary representation s is less than or equal to the positive integer with binary representation t. a) Determine if (A, ≼) is a partial order. b) If you determined that (A, ≼) is a partial order, then investigate if (A, ≼) is a total order. If you determined that (A, ≼) is not a partial order, then indicate the properties of a partial order that (A, ≼) lacks.

Let A be the set of all binary strings of length 3. Let ≼be a relation on A such that for any s ∈A and t ∈A, s ≼t if and only if the positive integer with binary representation s is less than or equal to the positive integer with binary representation t. a) Determine if (A, ≼) is a partial order. b) If you determined that (A, ≼) is a partial order, then investigate if (A, ≼) is a total order. If you determined that (A, ≼) is not a partial order, then indicate the properties of a partial order that (A, ≼) lacks.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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