An integer n is called even if n = 2m for some integer m, and...
50.1K
Verified Solution
Link Copied!
Question
Advance Math
An integer n is called even if n = 2m for some integer m, and odd if n + 1 is even. Prove the following statements:
(a) An integer cannot be both even and odd.
(b) Every integer is either even or odd.
(c) The sum or product of even integers is an even integer. What can you say about the sum or product of odd integers?
Answer & Explanation
Solved by verified expert
4.3 Ratings (748 Votes)
a If an integer is both even and odd there exist integers m and n such that 2m 2n 1 This implies that 1 2mn which means that 1 is even but this is a contradiction since 1 0 1 is odd Hence every integer is either ever or odd b Suppose on the contrary that the set S k Z k is neither even nor odd is
See Answer
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
