2026-09-10T00:15:25.932787 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Work through all four parts of this question abou...
Question 1 Report
Work through all four parts of this question about the numbers \(1\) to \(15\). Set \(A\) is the multiples of \(3\) and set \(B\) is the even numbers.
(a) Complete the Venn diagram in the figure by writing each of the \(15\) numbers in the correct region. [2]
(b) Write down the numbers that are in both set \(A\) and set \(B\). [1]
(c) State how many of the numbers are in neither set. [1]
(d) Work out the fraction of the \(15\) numbers that are in set \(A\) or set \(B\) or both. Give your fraction in its simplest form. [2]
Answer Details
Set \(A\) contains multiples of \(3\), and set \(B\) contains even numbers. The numbers in both sets must be both multiples of \(3\) and even.
- (a) The completed Venn diagram is shown below. The overlap contains \(6\) and \(12\); these are the even multiples of \(3\). [B1] All remaining numbers are placed according to whether they meet neither, one, or both rules. [B1]
- (b) The numbers in both \(A\) and \(B\) are \(6\) and \(12\). [B1]
- (c) There are \(5\) numbers in neither set: \(1,5,7,11,13\). [B1]
- (d) The union contains \(3\) numbers in \(A\) only, \(2\) in both, and \(5\) in \(B\) only:
\[3+2+5=10.\] [M1]
The required fraction is \[\frac{10}{15}=\frac23.\] [A1]
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