What This Document Is
This document is Part A of an examlet for CS 173, Discrete Structures, offered at the University of Illinois at Urbana-Champaign. It’s designed to assess your understanding of fundamental concepts related to functions and their properties within the realm of discrete mathematics. This particular examlet focuses on applying definitions and proving properties of functions, rather than computational exercises.
Why This Document Matters
This resource is invaluable for students currently enrolled in a Discrete Structures course, particularly those preparing for assessments. Working through similar problems will help solidify your grasp of core concepts and improve your ability to construct rigorous mathematical proofs. It’s most beneficial to use this examlet as a practice tool *after* you’ve studied the relevant course materials and are looking for ways to test your understanding and identify areas for improvement. It's also useful for understanding the expected format and difficulty level of exams in this course.
Topics Covered
* Function definitions and notation
* One-to-one (injective) functions
* Onto (surjective) functions
* Function composition and operations
* Proof techniques in discrete mathematics
* Working with integer and natural number sets
* Absolute value and its properties
What This Document Provides
* Multiple problems requiring proofs related to function properties.
* Clear problem statements defining specific functions and their domains.
* Space for students to write their solutions.
* A structured format mirroring typical exam questions in the course.
* An opportunity to practice applying definitions directly to demonstrate understanding.
* Examples of how to approach problems involving function properties.
