Year 12 Maths Extension 2 (2027)
Proof
Induction – Geometric Results
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Questions
Question 1
183393
Prove by mathematical induction that a set with \(n\) elements has \(2^n\) subsets.
Base \(n=1\): \(\{a\}\) has \(2 = 2^1\) subsets. Step: each subset of a \((k+1)\)-element set either excludes or includes the new element, giving \(2\cdot 2^k = 2^{k+1}\) subsets.
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