Suggested languages for you:

Americas

Europe

Problem 1

Examine the following formal descriptions of sets so that you understand which members they contain. Write a short informal English description of each set. a. $$\\{1,3,5,7, \ldots\\}$$ b. $$\\{\ldots,-4,-2,0,2,4, \ldots\\}$$ c. $$\\{n \mid n=2 m$$ for some $$m$$ in $$\mathcal{N}\\}$$ d. $$\\{n \mid n=2 m$$ for some $$m$$ in $$\mathcal{N}$$, and $$n=3 k$$ for some $$k$$ in $$\mathcal{N}\\}$$ e. $$\\{w \mid w$$ is a string of os and 1 s and $$w$$ equals the reverse of $$w\\}$$ f. $$\\{n \mid n$$ is an integer and $$n=n+1\\}$$

Expert verified
a. Odd positive integers b. All even integers (positive, negative, and 0) c. Even positive integers d. Multiples of 6 e. Binary palindromes f. Empty set (∅)
See the step by step solution

Step 1: a. Set A: {1, 3, 5, 7, ...}

This set contains all odd positive integers. They can be described as integers which are not divisible by 2.

Step 2: b. Set B: {..., -4, -2, 0, 2, 4, ...}

This set contains all even integers, both positive and negative, as well as 0. They can be described as integers which are divisible by 2.

Step 3: c. Set C: {n | n = 2m for some m in ℕ}

This set contains all the even positive integers. It contains the numbers obtained by multiplying any natural number m by 2.

Step 4: d. Set D: {n | n = 2m for some m in ℕ, and n = 3k for some k in ℕ}

This set contains all positive integers that are both multiples of 2 and 3. These numbers can also be described as multiples of 6, since the least common multiple of 2 and 3 is 6.

Step 5: e. Set E: {w | w is a string of 0s and 1s and w equals the reverse of w}

This set contains binary strings (strings made up of 0s and 1s) which read the same forwards and backwards. These strings are called palindromes.

Step 6: f. Set F: {n | n is an integer and n = n + 1}

This set is actually empty (denoted by ∅), as it contains no elements. The given condition (n = n + 1) is not possible for any integer, as it would mean that 1 is equal to 0, which is a contradiction.

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner