Six original Cambridge-style questions on sets and Venn diagrams: notation, listing, two-set and (Extended) three-set problems.
(a) \(\xi = \{1, 2, \dots, 15\}\) and \(A = \{x : x \text{ is a prime number}\}\). List the elements of A and write down \(n(A)\).
(b) List the elements of \(\{x : x \text{ is an integer},\ -2 < x \le 3\}\).
\(\xi = \{1, 2, \dots, 16\}\), \(A = \{\text{odd numbers}\}\) and \(B = \{\text{square numbers}\}\).
(a) List \(A \cap B\). (b) Find \(n(A \cup B)\). (c) List \(A' \cap B\).
50 people were asked whether they drink tea (T) or coffee (C). 28 drink tea, 23 drink coffee and 9 drink neither.
(a) Find how many drink both. (b) Find \(n(T \cap C')\) and say what it means.
Describe in words the elements of (a) \(A \cap B\) (b) \((A \cup B)'\).
(Extended) \(\xi = \{x : x \text{ is an integer},\ 1 \le x \le 10\}\), \(E = \{\text{even numbers}\}\) and \(F = \{x : x > 6\}\).
(a) List \(E \cap F\). (b) Is \(\{8, 10\} \subseteq E\)? Give a reason. (c) Complete with \(\in\) or \(\notin\): \(7 \ \_\_\ E\). (d) Find \(n(E' \cap F')\).
(Extended) 50 students were asked which of Art (A), Biology (B) and Chemistry (C) they study. 3 study all three. 5 study Art and Biology only, 4 study Art and Chemistry only, and 6 study Biology and Chemistry only. \(n(A) = 20\), \(n(B) = 22\) and \(n(C) = 18\).
Find (a) the number who study exactly one of the subjects (b) the number who study none of them.
Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.