CSCI 301 L02 Worksheet

Lecture 2 - Exercises

Part A

Write down each of the following sets using the roster method:

  1. \(V\), the set of all vowels in the English alphabet; for our purposes, we won’t include y as a vowel.
  2. \(O\), the set of all positive integers less than 10
  3. \(S\), the set of all positive integers less than 100
  4. The set of all integers

True or false:

  1. \(0 \in \mathbb{Z}\)
  2. \(0 \in \mathbb{N}\)
  3. \(V = \{u, i, a, e, o, u\}\) (using \(V\) as defined above in Part A)
  4. \(\pi \in \mathbb{Q}\)

Part B - Set Builder Notation

Write the following sets in set builder notation:

  1. All the odd integers
  2. All the natural numbers that are perfect squares
  3. All the squares of odd integers
  4. The set of positive rational numbers

Part C - Cardinality

  1. Let \(S = \{n^2 : n \in \mathbb{Z}\}\). Is \(S\) finite or infinite?
  2. What is \(|\{2k + 1 : k \in \mathbb{Z^+} \text{ and } k < 5\}|\)?
  3. What is |\(\varnothing\)|?
  4. What is \(|\{\varnothing\}|\)?
  5. What is \(|\{\varnothing, \{\{\varnothing\}\}\}|\)?