Answered: 1. If n is odd, prove that n+1 is even.…

1. If n is odd, prove that n+1 is even. 2. If a is a multiple of 6 and b is a multiple of 9, prove that a-b is a multiple of 3. 3. Suppose x satisfies 1 ≤ x ≤ 3. Prove that x² - 4x < 0.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

1. If n is odd, prove that n+1 is even.
2. If a is a multiple of 6 and b is a multiple of 9, prove that a-b is a multiple of 3.
3. Suppose x satisfies 1 ≤ x ≤ 3. Prove that x² - 4x < 0.

Expert Solution

Step 1

1. Here given that n is odd. Let us consider n is the form of (2k+1) where $k \in ℤ .$

So now n+1 = 2k+2 = 2(k+1) which is a multiple of 2 for all $k \in ℤ .$

So n+1 is even if n is odd.

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