PROBLEM 7: Binary Relations, Functions and Orderings (15 pts)1. (2 pts) Prove that ({2, 3, 4, 6, 24, 36, 72}, /) is a poset, create its corresponding Hassediagram and identify maximal and minimal elements.2. (1 pts) Prove that (P{1, 2, 3}, C) is a poset, create its corresponding Hasse diagramand identify maximal and minimal elements3. Assume the following mapping, captured by variable map:map ={72 {1,2,3},36{3},24 {1,2},6- → {3},4 {1,3},2➡ {}}Provide answers to the following in detail (in plain english and formally):(a) (2 pts) Is variable map a function? If so, is it a total or a partial function? Identifydomain and codomain.(b) (10 pts) Discuss all properties (injectivity, surjectivity, bijection, order preserving,order reflecting, order embedding, isomorphism).NOTE: When we reason formally on a property we must state: (1) What Law do we expectto hold or not hold, and (2) Does this Law indeed hold or Is this Law violated?

1. Proof that ({2,3,4,6,24,36,72},/) is a Poset A partially ordered set (poset) is a set with a…

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 33EQ

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