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It requires computing logical equivalence via full truth tables, deriving valid/invalid conclusions, and providing predicate-logic encodings of natural-language statements. Additional tasks include induction proofs, identifying errors in a faulty proof by contradiction, and constructing a Tarski World subject to specified relations and color constraints.",{"@graph":69,"@context":122},[70,84,105],{"@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/midterm-reasoning-and-logic-cse1300-exam/459377/",{"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/midterm-reasoning-and-logic-cse1300-exam/459377.png","ImageObject",300,407,{"name":92,"@type":93},"Danger Angel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is the exam grade computed and what is the passing requirement?","Question",{"text":112,"@type":113},"The grade is computed as 1 + 9/68 times the total points. A grade of at least 5 out of 10 is required to pass, assuming the average course grade is at least 5.75.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Are external resources allowed during the exam?",{"text":117,"@type":113},"No. The use of the book, notes, calculators, or other sources is strictly prohibited.",{"name":119,"@type":110,"acceptedAnswer":120},"What should be done before submitting the exam paper?",{"text":121,"@type":113},"Before handing in answers, check that every sheet contains your name and student number.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},459377,1790755808,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":39,"preview_page_count":4},962090769052,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Midterm Reasoning and Logic (CSE1300)  \nExam created by Stefan Hugtenburg & Neil Yorke-Smith  \nPlease read the following information carefully!  \n􀀏 This exam consists of 8 open questions. The open questions are worth a total of 68 points and the points per open (sub) question are given in the (sub) question itself.  \nscore  \n􀀏 The grade for this exam is computed as 1 + 9 􀀁 68 . Note that you require a grade of at least 5 out of 10 to pass the course (assuming your average course grade is at least 5 .75) .  \n􀀏 This exam corresponds to chapters 1 to 3 of the book Delftse Foundations of Computation (version 1. 1), with the exception of the topic of structural induction.  \n􀀏 You have 120 minutes to complete this exam.  \n􀀏 Before you hand in your answers, check that every sheet of paper contains your name and student number.  \n􀀏 The use of the book, notes, calculators or other sources is strictly prohibited.  \n􀀏 Read every question properly and in the case of the open questions, give all information requested. Do not however give irrelevant information, this could lead to a deduction of points.  \n􀀏 You may write on this exam paper and take it home.  \n􀀏 Exam is 􀀍c2019 TU Delft.  \n\n| Question: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Total: |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Points: | 12 | 7 | 8 | 6 | 7 | 6 | 17 | 5 | 68 |\n\n1. (a) (2 points) Create a truth table for: : (p $ q) _ (:p ^ q) .  \n(b) Consider a new type of operator that operates on three propositions at a time. This ternary operator is de􀀌ned by the following truth table:  \np q r  p ! r  \n0 0 0  0 0 0 1  1 0 1 0  0 0 1 1  1 1 0 0  1 1 0 1  0 1 1 0  0  \n1 1 1  1  \nSomeone argues that (q 􀀀 q) _ r 􀀑 :(p _ r) ! r holds.  \ni. (6 points) Create the full truth table for both propositions.  \nii. (1 point) Describe how we can derive the (in)validity of this equivalence from your truth table.  \n(c) (3 points) Rewrite (p _ q) ! : (r ^ q) to DNF. Simplify your result as much as possible.  \n2. For each of the following claims, either explain why they are true, or give a counterexample. Start your answer with either the word \\True\" or \\False\" indicating which of the two options applies.  \n(a) (2 points) It is not possible for some proposition p to be both su􀀎cient and necessary for some proposition q.  \n(b) (2 points) Every argument that can be represented in propositional logic, can be represented in predicate logic.  \n(c) (3 points) You can prove a property P (x) holds for all even integers 􀀕 3 using induction. If you answer true, explain what the base case and induction step should look like. If you answer false, give a counterexample and a brief explanation.  \n3. For this question you need to translate claims from natural language to predicate logic. Make sure to de􀀌ne all predicates you introduce and to include all of the information from the original statement in your translation.  \n(a) (2 points) Stefan loves CSE1300 .  \n(b) (3 points) There is a TA that has a blue badge.  \n(c) (3 points) When you grade an exam, you eat a pepernoot.1  \n4. Translate the following two claims to natural language (English) . The predicates and domain used in our claims are as follows:  \n􀀏 The domain of discourse is \\all objects\" (including living beings) .  \n􀀏 Song (x) means: x is a song.  \n􀀏 Artist (x) means: x is an artist.  \n􀀏 Better (x; y) means: x is better than y.  \n􀀏 Performs (x; y) means: x performs y.  \n􀀏 t is Tom Lehrer.  \n􀀏 e is The Element Song.  \n(a) (1 point) Song (e) ^ :Artist(e)  \n(b) (1 point) :9x(Artist(x) ^ Better(x; t)) .  \n(c) (4 points)  \n8x((Song(x) ! 9y(Artist(y) ^ Performs(y; x))) ^ (Artist(x) ! 9y(Song(y) ^ Performs(x; y))))  \n5. (a) (4 points) Consider the following set of predicates over the domain D = f1; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10g.  \n􀀏 8x(P(x) $ (x j 2))  \n􀀏 8x(Q(x) $ 9z(z \u003C 4 ^ (3 j (x + z))))  \n􀀏 8x8y(R(x; y) $ ((x = y + 2) ^ 9z((z > 4) ^ (x j (z + y))))) Give the truth sets for P , Q, and R.  \n1 \\A pepernoot\" is a small \\cookie\" Dutch","cbCaieommt5oyjB7","https://ap.wps.com/l/cbCaieommt5oyjB7","pdf",147851,"English","# Question 1\n## (a) Truth table and ternary operator argument\n## (b) Truth table equivalence derivation and validity description\n## (c) DNF conversion and simplification\n# Question 2\n## Prove or refute sufficiency/necessity, logic translation, and induction claim\n# Question 3\n## Translate natural language claims into predicate logic\n# Question 4\n## Translate predicate-logic claims into natural language\n# Question 5\n## (a) Truth sets for predicates P, Q, R\n## (b) Draw a Tarski World meeting given criteria\n# Question 6\n## (a) Check validity of a first-order argument\n## (b) Check satisfiability of a set of predicates\n# Question 7\n## (a) Induction proof about parity\n## (b) Prove a divisibility claim using positive integers\n## (c) Diagnose mistakes in a faulty proof by contradiction\n# Question 8","[{\"question\":\"How is the exam grade computed and what is the passing requirement?\",\"answer\":\"The grade is computed as 1 + 9/68 times the total points. A grade of at least 5 out of 10 is required to pass, assuming the average course grade is at least 5.75.\"},{\"question\":\"Are external resources allowed during the exam?\",\"answer\":\"No. The use of the book, notes, calculators, or other sources is strictly prohibited.\"},{\"question\":\"What should be done before submitting the exam paper?\",\"answer\":\"Before handing in answers, check that every sheet contains your name and student number.\"}]","Midterm Reasoning and Logic (CSE1300) - Exam | PDF"]