Sets and Venn diagramsIB MYP Maths Standard: Mind map

Exam questions on Sets and Venn diagrams

1. The universal set is $\xi=\{1,2,3,4,5,6,7,8,9,10,11,12\}$. Set $A$ is the set of even numbers in $\xi$ and set $B$ is the set of multiples of 3 in $\xi$.
   List the elements of $(A\cup B)'$.2 marks
2. In a group of 44 students at an international school in Doha, 22 play football ($F$), 18 play basketball ($B$) and 8 play both sports. A student is chosen at random from the group.
   Find the probability that the student plays exactly one of the two sports.2 marks
3. A survey of 50 tourists in Istanbul asks which of three sites they visited: Hagia Sophia ($H$), Topkapi Palace ($T$) and the Basilica Cistern ($C$). $n(H)=22$, $n(T)=20$, $n(C)=18$. Also $n(H\cap T)=8$, $n(H\cap C)=9$ and $n(T\cap C)=7$, and each of these includes the 5 tourists who visited all three sites.
   Find the number of tourists who visited exactly two of the three sites.3 marks