Drawing two sets from their elements
Drawing two sets from their elements
Secondary 4
8 marks
\(\xi=\{x: x \text{ is an integer}, 1\le x\le 12\}\), \(A=\{x: x \text{ is a multiple of}\hspace{0.5em} 3\}\), \(B=\{x: x \text{ is a multiple of}\hspace{0.5em} 6\}\) and \(C=\{x: x \text{ is a factor of}\hspace{0.5em} 10\}\).
- List the elements of \(A\), \(B\) and \(C\).[2]
- Draw a Venn diagram to show \(\xi\), \(A\) and \(B\), placing every element of \(\xi\) in its region.[2]
- Draw a Venn diagram to show \(\xi\), \(A\) and \(C\), placing every element of \(\xi\) in its region.[2]
- Using set notation, state the relationship between \(B\) and \(A\), and the relationship between \(A\) and \(C\).[2]
Solution:
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Answer:(a) \(A=\{3,6,9,12\}\), \(B=\{6,12\}\), \(C=\{1,2,5,10\}\) (b) \(B\) inside \(A\); \(B\): \(6,12\); \(A\) only: \(3,9\); outside \(A\): \(1,2,4,5,7,8,10,11\) (c) \(A\) and \(C\) apart; \(A\): \(3,6,9,12\); \(C\): \(1,2,5,10\); outside both: \(4,7,8,11\) (d) \(B\subset A\); \(A\cap C=\varnothing\)
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