et S ⊆ N, and for any a, b ∈ N, consider a relation R such that aRb if and only if there exists c ∈ S such that a + c = b. Show that if R is a partial order, then (i) 0 ∈ S (ii) for any a, b ∈ S, a + b ∈ S. You do not need to write a formal proof – a clear, concise and correct justification is sufficient.

et S ⊆ N, and for any a, b ∈ N, consider a relation R such that aRb if and only if there exists c ∈ S such that a + c = b. Show that if R is a partial order, then (i) 0 ∈ S (ii) for any a, b ∈ S, a + b ∈ S. You do not need to write a formal proof – a clear, concise and correct justification is sufficient.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 18E: Let R be the relation defined on the set of integers by aRb if and only if ab. Prove or disprove...

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