Relations Functions
1. Let's start by understanding what a relation is. A relation between two sets is a collection of ordered pairs where the first element is from the first set and the second element is from the second set.
2. A function is a special type of relation where each element in the first set (domain) is related to exactly one element in the second set (codomain).
3. To determine if a relation is a function, check if any input (first element) corresponds to more than one output (second element). If yes, it's not a function.
4. For example, if we have a relation \( R = \{(1,2), (2,3), (3,4)\} \), each input maps to exactly one output, so \( R \) is a function.
5. If the relation is \( S = \{(1,2), (1,3), (2,4)\} \), the input 1 maps to two outputs (2 and 3), so \( S \) is not a function.
6. For your questions, please provide the specific relations or functions you want to analyze or work with, and I can help you solve or understand them step-by-step.