[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-273377-105":59,"doc-detail-273377-en":123},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","mathematical-logic-exercises","Mathematical Logic Exercises","","A set of guided practice problems for mathematical logic, designed to reinforce lecture topics on propositional logic, first order logic, and modal logic. The booklet focuses on forming well-defined logical formulas, checking satisfaction under given interpretations, and computing truth tables. It provides structured exercise sets with solutions, including reductions to normal forms and work on satisfiability and validity within modal systems. The material supports understanding and mastery through step-by-step logical analysis.",{"@graph":69,"@context":115},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematical-logic-exercises/273377/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematical-logic-exercises/273377.png","ImageObject",300,407,{"name":92,"@type":93},"Maeve","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"How are the exercises supported for independent study?","Question",{"text":113,"@type":114},"Each exercise is accompanied by solution information, helping learners verify results and strengthen mastery aligned with course lectures.","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},273377,1789471143,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":16,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":122,"read_time":136},5909877438554,"https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272","MATHEMATICAL LOGIC EXERCISES  \nChiara Ghidini and Luciano Serafini  \nAnno Accademico 2013-2014  \nWe thank Annapaola Marconi for her work in previous editions ofthis booklet.  \nEverything should be made as simple as possible, but not simpler.  \nReader's Digest. Oct. 1977 Albert Einstein  \nContents  \n1 Introduction 3  \n2 Propositional Logic 5  \n2.1 Basic Concepts ............................. 5  \n2.2 Truth Tables .............................. 6  \n2.3 Propositional Formalization ..................... 10  \n2.3.1 Formalizing Simple Sentences ................ 10  \n2.3.2 Formalizing Problems .................... 17  \n2.4 Normal Form Reduction ....................... 28  \n3 First Order Logic 31  \n3.1 Basic Concepts ............................. 31  \n3.2 FOL Formalization .......................... 35  \n4 Modal Logic 55  \n4.1 Basic Concepts ............................. 56  \n4.2 Satisfiability and Validity ...................... 63  \n4.3 Modal Logic Formalization ...................... 76  \nChapter 1  \nMathematics is the only instructional material that can be presented in an entirely undogmatic way.  \nThe Mathematical Intelligencer, v. 5, no. 2, 1983 MAX DEHN  \nIntroduction  \nThe purpose of this booklet is to give you a number of exercises on propositional, first order and modal logics to complement the topics and exercises covered during the lectures of the course on mathematical logic. The material presented here is not a direct component of the course but is offered to you as an incentive and a support to understand and master the concepts and exercises presented during the course.  \n\n| Symbol | Difficulty |\n| --- | --- |\n\n\n| ✏\u003Cbr>✣\u003Cbr>✛\u003Cbr>✜\u003Cbr>✚ | Trivial Easy Medium Difficult\u003Cbr>Very difficult |\n| --- | --- |\n\nChapter 2  \nWhen you have eliminated the impossible, what ever remains, however improbable must bethe truth.  \nThe Sign of Four. SIR ARTHUR CONAN DOYLE  \nPropositional Logic  \n2.1 Basic Concepts  \nExercise 2.1. ✣ -  \nWhich of the following are well formed propositional formulas?  \n1. _pq  \n2. (: (p ! (q ^ p)))  \n3. (: (p ! (q = p)))  \n4. (: (􀀆(q _ p)))  \n5. (p ^ :q) _ (q ! r)  \n6. p:r  \nSolution.  \nWell formed formulas: 2. and 5.  \n]  \nExercise 2.2. ✣ -  \nLet's consider the interpretation v where v(p) = F, v (q) = T, v (r) = T. Does v satisfy the following propositional formulas?  \n1. (p ! :q) _ : (r ^ q)  \n2. (:p _ :q) ! (p _ :r)  \n3. : (:p ! :q) ^ r  \n4. : (:p ! q ^ :r)  \nSolution.  \nv satisfies 1., 3. and 4.  \nv doesn't satisfy 2.  \n2.2 Truth Tables  \nExercise 2.3. ✣ -  \nCompute the truth table of (F _ G) ^ : (F ^ G).  \nSolution.  \n\n| F | G |  | F _ G | F ^ G | : (F ^ G) | (F _ G) ^ : (F ^ G) |\n| --- | --- | --- | --- | --- | --- | --- |\n\n\n| T\u003Cbr>T\u003Cbr>F\u003Cbr>F | T\u003Cbr>F\u003Cbr>T\u003Cbr>F | T\u003Cbr>T\u003Cbr>T\u003Cbr>F | T\u003Cbr>F\u003Cbr>F\u003Cbr>F | F\u003Cbr>T\u003Cbr>T\u003Cbr>T | F\u003Cbr>T\u003Cbr>T\u003Cbr>F |\n| --- | --- | --- | --- | --- | --- |\n\n+ The formula models an exclusive or!  \n]","cbCaihPWUWmFOkjX","https://ap.wps.com/l/cbCaihPWUWmFOkjX","pdf",374907,"English","# Introduction\n# Propositional Logic\n## Basic Concepts\n## Truth Tables\n## Propositional Formalization\n## Normal Form Reduction\n# First Order Logic\n## Basic Concepts\n## FOL Formalization\n# Modal Logic\n## Basic Concepts\n## Satisfiability and Validity\n## Modal Logic Formalization","[{\"question\":\"How are the exercises supported for independent study?\",\"answer\":\"Each exercise is accompanied by solution information, helping learners verify results and strengthen mastery aligned with course lectures.\"}]","Mathematical Logic Exercises | PDF",202]