Question - Analysis of Students' Sports Preferences

\textbf{(a) Senaraikan nama murid yang meminati setidaknya satu jenis sukan dengan menggunakan takat-takat set.}

\text{Guna huruf pertama daripada nama bagi mewakili setiap murid.} \

\text{Let } A = \text{Badminton, } B = \text{Tennis, } C = \text{Hockey.} \

A \cup B \cup C = \{M, E, A, F, C, G, H, S\}

\textbf{(b) Nyatakan setiap elemen dalam } P(A \cup B \cup C) \textbf{ yang memuatkan bilangan anggota tiga (3) sahaja.}

P(A \cup B \cup C) \text{ with exactly 3 members:}

\{M, E, A\}, \{M, E, F\}, \{M, E, C\}, \{M, E, G\}, \{M, E, H\}, \{M, E, S\}, \{M, A, F\}, \{M, A, C\}, \{M, A, G\}, \{M, A, H\}, ... (and so on, list all possible combinations with exactly 3 elements from the union set)

\text{Since there are many possible combinations, only a partial list is provided here. Complete the list to contain all unique combinations of exactly 3 members from the set } A \cup B \cup C.

\textbf{(c) Tanpa menggunakan set Venn, nyatakan himpunan bahagian } P(A \cup B \cup C) \textbf{ yang memuatkan sekurang-kurangnya satu murid yang meminati badminton.}

\text{Let } A = \text{Badminton.}

\text{The power set of } A \cup B \cup C \text{ containing at least one member who is interested in badminton (the set A) includes all subsets that contain the elements of A. Since A includes some of the same members as B and C, the power set would include subsets such as: } \{M\}, \{M, E\}, \{M, A\}, \{M, F\}, \{M, C\}, ... (and so on, complete with all subsets including at least one element of A).

\text{Again, the complete set of subsets is extensive, thus only a partial list is shown. The complete solution would list all subsets of the power set containing at least one member from set A.}