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Question on propositional logic Part A Alexandre, Chen, Lina, Nour and Wassim are friends and, if they cannot meet inperson, they sometimes find themselves private discussion group At giventimet we know that the following propositions true: P1: From Chen and Lina, atleast one of the two online P2: Nour o Wassimis online but not both; P3: f Alexandre isonline, then Nour too; P4: From Chen and Wassim, either the rone P5: flinaisonline then Alexander Chen 1. Express each of the propositions PltoP5 only logica connectors and five simple propositions that you will define 2. Determine with justification, whoi online the given time Answer: Part B Let S be the expression: "IFSistrue, then the centaurs exist" Show thatifsisalogical proposition, then the proposition "Centaurs exist" is true. Deduce that cannot be a proposition. Answer: Question 2on the logic of predicates Consider the following .P(x): "Student knows ++". .Q(x "Student " where theuniverse speechof of students nompute universeo speech ofyis the set of course groups of the IT 1 Write Some Answer (b)Notal students can program Answer (c)Eachcourse ++, (e) (f) There 2. Constraint but compound expression 3. Expresseech of the Answer (i) xx, P(x) >Q(x.y) Answer Answer Answer Question 3 on sets Parts and are independent. Part A Let A.B.Cbe sets. Usingamembershiptable, determineif Answer: Part B For say true false, Answer Answer Answer Answer: andAnD=d thenBnC=d Answer: AUB em AnB : B Answer Answer Question on sets and counting Let A Band bethree subsets ofthe universal set whichsatish the following Sconditions (a) 9(AnBnC) 128 (b) 17 (c) |AnC = 12 (d) |AnB|=14 (e) A = BB - -1 (f) |B@C==55 (g) (h) AnBnd=19(10)(1) Determine the cardinalities the sets B.0 andUby carefully justifying your reasoning Answer:

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