Take \(\mathcal{E}\) to be every whole number strictly between 10 and 30. \(C = \{x : x \text{ is a multiple of 9}\}\) and \(D = \{x : x \text{ is an even n...
Question 1 Report
Take \(\mathcal{E}\) to be every whole number strictly between 10 and 30.
\(C = \{x : x \text{ is a multiple of 9}\}\) and \(D = \{x : x \text{ is an even number}\}\). The number line below shows the elements of \(D\) within \(\mathcal{E}\).
- List the elements of \(C\). (2)
- List the elements of \(C \cup D\). (2)
- Write down \(n(D')\). (1)
Answer Details
This question lists a set defined by a divisibility rule, reads a second set from a number line, then finds their union and a complement.
(a) The universal set is every whole number strictly between 10 and 30 (11 to 29 inclusive). Listing the multiples of 9 in this range: \[ C = \{18, 27\} \] [2 marks]
(b) Reading the even numbers marked on the number line: \(D = \{12, 14, 16, 18, 20, 22, 24, 26, 28\}\). Combining \(C\) and \(D\) without repeating the shared value 18: \[ C \cup D = \{12, 14, 16, 18, 20, 22, 24, 26, 27, 28\} \] [2 marks]
(c) There are 19 numbers in the universal set (11 to 29 inclusive), and \(n(D) = 9\), so: \[ n(D') = 19 - 9 = 10 \] [1 mark]
Since 18 is both a multiple of 9 and even, it appears in both \(C\) and \(D\); when forming the union, it is written into the combined list only once, not twice.
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