Question on propositional logic
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
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
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
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
(i) xx, P(x) >Q(x.y)
Question 3 on sets
Parts and are independent.
Let A.B.Cbe sets. Usingamembershiptable, determineif
AUB em AnB : B
Question on sets and counting
Let A Band bethree subsets ofthe universal set whichsatish the following Sconditions
(a) 9(AnBnC) 128
(c) |AnC = 12
(e) A = BB - -1
Determine the cardinalities the sets B.0 andUby carefully justifying your reasoning
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