1. 1
   The universal set is $\mathcal{E} = \{1,2,3,...,12\}$. Set $A = \{3,6,9,12\}$ (multiples of 3). Set $B = \{4,8,12\}$ (multiples of 4).

   (a)

   Find $n(A \cap B)$.

   [1 mark]

   • A0
   • B1
   • C2
   • D3

   (b)

   Find $n(A \cup B)$.

   [1 mark]

   • A5
   • B6
   • C7
   • D8

   (c)

   Find $n(A')$.

   [1 mark]

   • A6
   • B7
   • C8
   • D9

   Total for question 1: 3 marks

2. 2
   In a class of 30 students, $P$ is the set of students who play football and $T$ is the set of students who play tennis. 18 students play football, 12 play tennis, and 5 play both football and tennis.

   (a)

   Find the number of students in the class who play neither football nor tennis.

   [2 marks]

   (b)

   Find the number of students who play football but not tennis.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Set $C = \{x : x \text{ is an integer}, 3 \leq x \leq 15\}$. Set $D = \{x : x \text{ is a multiple of } 4, x \in C\}$.

   (a)

   List the elements of set $D$, then find $n(C \cap D')$.

   [3 marks]

   (b)

   Given the universal set is $\mathcal{E} = \{x : x \text{ is an integer}, 1 \leq x \leq 20\}$, find $n(C')$, the number of elements in the complement of $C$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In a survey of 50 students: 28 study Physics ($P$), 24 study Chemistry ($C$), 20 study Biology ($B$). 12 study both Physics and Chemistry, 10 study both Chemistry and Biology, 8 study both Physics and Biology, and 5 study all three subjects.

   (a)

   Find the number of students who study Physics only.

   [4 marks]

   (b)

   Find the number of students who study Chemistry only.

   [4 marks]

   (c)

   Find the number of students who study none of the three subjects, and state $n(P \cup C \cup B)$.

   [5 marks]

   Total for question 4: 13 marks

End of questions