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Magazine Problem 15
Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it. These exercises are cumulative, covering all topics addressed in Chapters \(1-9 .\) Every odd integer is the sum of three odd integers.
Problem 20
Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it. These exercises are cumulative, covering all topics addressed in Chapters \(1-9 .\) There exist prime numbers \(p\) and \(q\) for which \(p-q=1000\).
Problem 24
Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it. These exercises are cumulative, covering all topics addressed in Chapters \(1-9 .\) The inequality \(2^{x} \geq x+1\) is true for all positive real numbers \(x\).
Problem 32
Each of the following statements is either true or false. If a statement is true, prove it. If a statement is false, disprove it. These exercises are cumulative, covering all topics addressed in Chapters \(1-9 .\) If \(n, k \in \mathbb{N}\) and \(\left(\begin{array}{l}n \\ k\end{array}\right)\) is a prime number, then \(k=1\) or \(k=n-1\).
