Why the number of subsets doubles
Why the number of subsets doubles
IP 2
8 marks
Let \(S_n\) be a set with \(n\) elements.
- List all the subsets of \(\{a,b,c\}\).[2]
- Explain why adding one new element to a set doubles its number of subsets. Hence state the number of subsets of \(S_n\).[2]
- Find the number of subsets of \(\{1,2,3,\ldots,10\}\) that contain \(1\) but do not contain \(2\).[2]
- One subset of \(\{1,2,3,\ldots,10\}\) is chosen at random, each subset being equally likely. Find the probability that it contains \(1\).[2]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) \(\varnothing\), \(\{a\}\), \(\{b\}\), \(\{c\}\), \(\{a,b\}\), \(\{a,c\}\), \(\{b,c\}\), \(\{a,b,c\}\) (b) Each old subset gives two new ones; \(2^n\) (c) \(256\) (d) \(\dfrac{1}{2}\)
Need help? Join our IP Math tuition programme.
Learn more