Multiples of 4 or 6 in a growing universal set
Multiples of 4 or 6 in a growing universal set
IP 2
8 marks
For a positive integer \(N\), let \(\xi=\{1,2,3,\ldots,N\}\), \(A=\{x\in\xi:x\text{ is a multiple of}\hspace{0.5em}4\}\) and \(B=\{x\in\xi:x\text{ is a multiple of}\hspace{0.5em}6\}\).
- For \(N=60\), find \(n(A)\), \(n(B)\) and \(n(A\cap B)\), and describe the elements of \(A\cap B\).[3]
- For \(N=60\), a number is chosen at random from \(\xi\). Find the probability that it lies in \(A\cup B\).[2]
- Find the least value of \(N\) for which \(n(A\cup B)\ge50\).[3]
Solution:
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Answer:(a) \(15\), \(10\), \(5\); multiples of \(12\) (b) \(\dfrac{1}{3}\) (c) \(N=150\)
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