Question 4. Let’s suppose that we are interested in writing some formal proposit

Question

Question 4. Let’s suppose that we are interested in writing some formal propositions about a bunch of people, some of whom are students in a school (called the U) and a bunch of courses, some of which are offered by the U.

• C(s): s is an offered course at the U
• S(x): x is a student (at the U)
• E(x, s): student x is enrolled in course s • F(x,y):xisafriendofy

For example, to write that there is an enrolled student who has a friend that is not a student, we could express that as:

xyz(S(x) C(z) E(x, z) ¬S(y) F (x, y))
Translate assertions (a) - (d) using only the predicates above, plus logical connectives, quantifiers, and equality

(between courses and between students, respectively).

(a) Every student at the U is enrolled in at least one course at the U.
(b) There is a course at the U that all students are enrolled in.
(c) Student x is enrolled in exactly 2 courses at the U. [x should be a free variable in your answer]. (d) When two students are friends, then they are enrolled in at least one course at the U in common.

(d) When two students are friends, then they are enrolled in at least one course at the U in common.

Explanation / Answer

Hi,
a. given every student is enrolled in a course, therefore
x z (S(x) / E(x,z))
b. there exists a course such that all students are enrolled means
y x C(y) /  E(x, y)
c. if 2 students are friends then they have a course common in U
s   x,y F (x, y) ->  E(y, s)= E(y, s)
if then is there, hence we use implciation.
Thumbs up if this was helpful, otherwise let me know in comments.

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