CM2010 Using the pigeonhole principle, prove that if we choose 14 different numbers from the following set {1, 2, 3, 4,…,20}: Fundamentals of Computer Science Assignment, NTU, Singapore

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University Nanyang Technological University (NTU)
Subject CM2010 Fundamentals of Computer Science Assignment

2) Using the pigeonhole principle, prove that if we choose 14 different numbers from the following set {1, 2, 3, 4,…,20}, then definitely there are two numbers such as a and b (among our 14 selected numbers) which their difference is at least 7 (i.e. |a-b| ≥7) [3 marks]

3) Prove the following statement by induction. For all positive integers n, prove 𝟐 𝟑𝒏 − 𝟏 is divisible by 7, State the mathematical induction and show your work clearly. [3 marks]

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