COS3761 Exam Practice #3 - Oct/Nov 2024 Paper, Question 2: Predicate Logic, Free Variables & Proofs

Session 3 of a student-led COS3761 (Formal Logic III, UNISA) exam practice series. We move on to Question 2 of the October/November 2024 paper: predicate logic. Translating quantified formulas, deciding what is a well-formed formula, drawing a parse tree to find free and bound variables, and a natural deduction proof with the existential quantifier. PAST PAPERS AND MODULE NOTES COS3761 page: studyhalo.com/modules/COS3761 More modules: studyhalo.com WHAT'S COVERED Q2.1 Predicate logic to English and back: read the atomic predicates first, then work from the inside out Rule of thumb: "for all" usually pairs with an implication, "there exists" with an "and" Q2.2 Well-formed formulas: functions can be arguments, formulas (predicates) cannot; is "for all x, there exists x" allowed? Q2.3 Parse tree, then mark every variable as free or bound (write the words, not just colours) Q2.4 Natural deduction with exists-elimination: open a box with a fresh variable x0, eliminate, re-introduce, close the box Exists-elimination: where the rule goes, compared with the textbook layout CHAPTERS 0:00 Plan for Question 2 and how the exam is structured 3:44 Q2.1 (i) Predicate logic to English 12:30 Q2.1 (ii) "Bob admires every student" in symbols 13:45 Tip: for all with implies, there exists with and 15:04 Q2.2 Which are well-formed formulas? 21:04 Can a predicate be an argument? 23:04 What the textbook says: use a parse tree 25:14 Q2.3 Drawing the parse tree 30:01 Marking free and bound variables 33:51 Q2.4 Natural deduction with exists 38:28 Fresh variable x0 and the proof box 45:42 Exists-elimination: textbook referencing compared 53:20 Past papers and module notes Previous: Session 2 - Jan/Feb 2023 paper, Question 1 [LINK] Playlist: [PLAYLIST LINK] Student-led study group, not official UNISA material. Check myUnisa and your tutorial letters for what is examinable. #COS3761 #UNISA #FormalLogic