question archive a) A directory contains a set of large files, L = {f1, f2, f3}, and set of data files, D = {d1, f2, a1000}, and a set of text files T = {t1, t2, f1, f2}
a) A directory contains a set of large files, L = {f1, f2, f3}, and set of data files, D = {d1, f2, a1000}, and a set of text files T = {t1, t2, f1, f2}
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a) A directory contains a set of large files, L = {f1, f2, f3}, and set of data files, D = {d1, f2, a1000}, and a set of text files T = {t1, t2, f1, f2}.
i. Give a set expression for the set of large data files, and write the set out.
ii. Repeat for the set of text files which are not large.
ili. Repeat for the set of large data files which are plain text.
iv . Repeat for the set of text files which are neither large nor data files.
b.All lecturers are well-informed and helpful. All well-informed lecturers prepare their classes well. Every lecturer who prepares his classes well has appropriate handouts and keeps to time. All helpful lecturers keep office hours. Everybody who has appropriate handouts and keeps office hours runs the risk of being taken advantage of by students who don't turn up to class. Therefore all lecturers run the risk of being taken advantage of by students who don't turn up to class." find a suitable universal set and predicates for each, express the hypotheses and conclusions in the language of predicate calculus.
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Answer:
In part a. we apply concept of intersection and union of sets, to solve
In part b, we formulate the predicates, find universal set and correspondingly express the hypothesis and conclusions
Step-by-step explanation
a. Large files = {f1, f2,f3}
Data files= {d1,f2,a1000}
Text files={t1,t2,f1,f2}
i) Large data files = {f2} {intersection of large files and data files}
ii) Text files not large= {t1,t2} {removing large files set from text files}
iii) Large data files, plain text = {f2} {Intersection of large, data and text files}
iv) Text files neither large nor data = {t1,t2} {removing large files and data files set from text files set}
b.
We choose as universe the set L of lecturers, and as predicates I(x), x is well-informed, H(x), x is helpful, P(x), x prepares his classes well, A(x), x has appropriate handouts, T(x), x keeps to time, O(x), x keeps office hours, R(x), x runs the risk of being taken advantage of by students to don't turn up to class. If we note that all quantification is over L, this gives hypotheses and conclusion:
(a) H1 : Vx I(x) AH(x)
(b) H2 : Vx I(x) = P(x)
(c) H3 : Vx H(x) = O(x)
(d) H4 : Vx P(x) = A(x)AT(x)
(e) H5: Vx|A(x)AO(x) = R(x) (f) C : Vx R(x)
