Cos3761 Assignment 1 (Complete Answers) 2024

COS3761 Assignment 1 (COMPLETE ANSWERS) 2024 ... 100 % TRUSTED workings, explanations and solutions. For assistance call or W.h.a.t.s.a.p.p us on +/ 2/ 5/ 4 /7 /7 /9 /5 /4 /0 /1 /3 /2 . ASSIGNMENT 1 Please note: There are 20 questions in this assignment. Choose 1 option out of 4 options. Assignment weighs 30% of the year mark Propositional logic symbol Declarative sentence associated with the symbol p Sam comes to the club q Susan comes to the club r Titus comes to the club s Bob comes to the club Table 1 QUESTION 1 Using the symbols and their intended meaning given in Table 1, which of the options below is a correct propositional logic translation of the following English sentence? It is not the case that Sam and Bob come to the club. Option 1:  (p  s) Option 2:  (p  s) Option 3: p  s Option 4:  p  s QUESTION 2 Using the symbols and their intended meaning given in Table 1 which of the options below is a correct propositional logic translation of the following English sentence? If Susan comes to the club then Bob and Sam come too. Option 1: p ∧ s → q Option 2: q → p ∧ s Option 3: (q → p) ∧ s Option 4: q ∧ p → s . Downloaded by Thomas Mboya () lOMoARcPSD| COS3761/102/0/2024 3 QUESTION 3 Using the symbols and their intended meaning given in Table 1, which of the options below is a correct propositional logic translation of the following English sentence? Bob comes to the club if and only if Susan comes and Titus does not come. Option 1: (s → q ∧ r) Option 2: (q ∧ r → s) Option 3: (s ↔ q ∧ r) Option 4: (q ∧ r ↔ s) QUESTION 4 Using the symbols and their intended meaning given in Table 1, which of the options below is a correct English translation of the following propositional logic sentence? ¬(s → ¬q) Option 1: It is the case that if Bob comes to the club then Susan comes. Option 2: It is not the case that if Bob comes to the club then Susan does not come. Option 3: It is the case that if Bob comes to the club then Susan comes. Option 4: It is not the case that if Bob comes to the club then Susan comes. QUESTION 5 Using the symbols and their intended meaning given in Table 1, which of the options below is a correct English translation of the following propositional logic sentence? A necessary condition for Susan coming to the club, is that, if Bob and Titus aren’t coming, Sam comes. Option 1: q → (¬s ∧ ¬r → p) Option 2: q → (¬s ∧¬ r ∧ p) Option 3: q ∧ p → (¬s ∧ ¬r ∧ p) Option 4: (¬s ∧ ¬r → p) → q QUESTION 6 Using the symbols and their intended meaning given in Table 1, which of the options below is a correct English translation of the following propositional logic sentence? (¬r ∧ ¬p) Option 1: Titus does not come to the club and Sam does not come to the club. Downloaded by Thomas Mboya () lOMoARcPSD| 4 Option 2: Titus does not come to the club and Sam comes to the club. Option 3: Titus and Sam come to the club. Option 4: Titus come to the club and Sam does not come to the club. QUESTION 7 Suppose you have to formally prove the validity of the following sequent using the basic natural deduction rules: p  q,  q ├ p Write out a proof on some rough paper and then choose the option below that gives a correct strategy. Option 1:  Start with the two premises p  q and  q.  Open an assumption box and assume p.  Using the copy rule, derive p.  Assume q.  Using the ¬ elimination rule, derive .  Derive p using the  elimination rule. Close the assumption box.  Derive p using the  elimination rule. Option 2:  Start with the two premises p  q and  q.  Open an assumption box and assume p.  Using the copy rule, derive p. Close the assumption box.  Open another assumption box and assume q.  Using the ¬ elimination rule, derive .  Derive p using the  elimination rule. Close the assumption box.  Derive p using the  elimination rule. Option 3:  Start with the two premises p  q and  q.  Open an assumption box and assume p.  Using the copy rule, derive p. Close the assumption box.  Open another assumption box and assume q.  Using the ¬ elimination rule, derive . Downloaded by Thomas Mboya () lOMoARcPSD| COS3761/102/0/2024 5  Close the assumption box.  Derive p using the  elimination rule. Option 4:  Start with the two premises p  q and  q.  Open an assumption box and assume p.  Using the copy rule, derive p.  Assume q.  Using the copy rule, derive p. Close the assumption box.  Derive p using the  elimination rule.