Question

Please answer the question (b)

For simplicity, assume that CUHK has only four colleges: Chung Chi, New Asia, United, and Shaw. Let C,N,U, and S be the sets of all Chung Chi students, New Asia students, United students, and Shaw students, respectively. Let M be the set of all Music Major students. Let Y be the sets of all students living in Ying Lin Tang (a Chung Chi hostel). Let W be the set of all students who attended the Wei Lun Lecture.

(a) Express the following in set-theoretic terms:

vi. Chung Chi Music Major students who attended the 2015 Wei Lun Lecture

(b) Show that for a student not belonging to Category vi in (a), if the student is a Music Major, then at least one of the following is true:

i. belongs to New Asia, United, or Shaw

ii. did not attend the Wei Lun Lecture.

Answer 1

If the student is a Music Major(M), then any student can be categorized as any one of the following:

{(C,M,W), (N,M,W), (U,M,W), (S,M,W), (C,M,W'), (N,M,W'), (U,M,W'), (S,M,W')}

Category vi in (a) are students with category (C,M,W)

Thus a student not belonging to Category vi in (a) can be in:

{(N,M,W), (U,M,W), (S,M,W), (C,M,W'), (N,M,W'), (U,M,W'), (S,M,W')}

In all these 7 possibilities, the student belongs to atleast one from either of

(i) New Asia, United, or Shaw or

(ii) did not attend the Wei Lun Lecture (i.e W')

(N,M,W), (U,M,W), (S,M,W) belongs to New Asia, United, or Shaw

(N,M,W'), (U,M,W'), (S,M,W') belongs to both New Asia, United, or Shaw and did not attend the Wei Lun Lecture

(C,M,W') belongs to did not attend the Wei Lun Lecture