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(a)If it is known that
students = {john, mary}
subjects = {co230, ca208}
and
.  X:students
pass(X,co230)
then we can deduce the following additional fact
pass(john,co230)  pass(mary,co230)
(i)For each of the following statements,state what additional facts
ay be deduced:
•~ X:students
pass(X,ca208)[1mark ]
•X:students
Y:subjects
pass(X,Y) [1mark ]
•X:students
Y:subjects
pass(X,Y) [1mark ]
•~X:subjects
pass(john,X) [1mark ]
(ii)Restate the following facts as quantified predicate expressions.
•~pass(john,ca208) .~pass(john,co230)
[1mark ]
•[pass(john,ca208) pass(john,co230)]
v[pass(mary,ca208) pass(mary,
co230)] [1mark ]
•pass(john,ca208) v pass(mary,ca208) [1mark ]
(b)Use the following
predicates to answer this part of the question.
taught_by(X,Y) X
is taughtbyY
teach_subject(X,Y) X
teaches the subject Y
pass(X,Y) X
passes the subject Y
(i)Restate the following expression as an English sentence:
X
Y
[taught_by(X, mark) teach_subject(mark,Y)]
=>pass(X, Y)
[2marks ]
(ii)Given that a student Karyn failed WW221,explain in English what
can be
concluded.You should use the given expression
X
Y
[taught_by(X, mark) teach_subject(mark,Y)]
=> pass(X, Y)
and show clearly all your working and the logical rules used.[4 arks
]
(iii)Given
X
Y
[taught_by(X, mark) .teach_subject(mark,Y)]
=>pass(X, Y)
and the knowledge that Joe passed WW221,explain if we can confidently
conclude that Mark teaches WW221 and that Joe was taught by Mark.[2
marks ]
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