CSCI 301 L00 Worksheet

Lecture 0 - Exercises

Outcomes:

Overview

• Get a sense for what the course is about
• Meet your classmates and set the tone for a collaborative, interactive learning environment

Sets 0

• Describe what a set is and how a set’s contents and members are denoted (\(\{\ldots\}\),\(\in\) )
• Know the notation for natural numbers (\(\mathbb{N}\)), integers (\(\mathbb{Z}\)), rational numbers (\(\mathbb{Q}\)), real numbers, and the empty set (\({\varnothing}\) or \(\emptyset\), or occasionally \(\{\}\))

Racket 0

• Know how to interpret and write expressions in prefix operator notation
• Know how to interact with the Racket interpeter in DrRacket
• Know how to represent and work with basic data types (booleans, numbers, strings) in racket.

Part A

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

1. \(V\), the set of all vowels in the English alphabet.
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

Part B

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 C

1. Recall that the formula for the volume of a sphere is \(\frac{4}{3}\pi r^3\). Racket has a built-in function expt to calculate exponents; its two arguments are the base and the exponent. Racket also has a built-in variable pi containing the (approximate) value of \(\pi\). Suppose a variable r has been defined, and write a Racket expression to compute the volume of a sphere with radius r.