1. Prove that (Z,, 1) is a commutative monoid using the formal definition of multiplication from the video. Furthermore, prove that multiplication distributes over addition in the integers. Hint: You first need to show that given u,v € Nx N, d(uv) = d(u)d(v) (this is similar to how, in the video, we proved d(u+v) = d(u) + d(v)). Doing this will make your life dramatically easier in the proof. Hint 2: Let up (n,n) n E N. What is d(vuo)?

1. Prove that (Z,, 1) is a commutative monoid using the formal definition of multiplication from the video. Furthermore, prove that multiplication distributes over addition in the integers. Hint: You first need to show that given u,v € Nx N, d(uv) = d(u)d(v) (this is similar to how, in the video, we proved d(u+v) = d(u) + d(v)). Doing this will make your life dramatically easier in the proof. Hint 2: Let up (n,n) n E N. What is d(vuo)?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 87E

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