Discrete Structures Question on a Relation

In summary, the problem is to define a relation R on the set A of all strings of a's and b's of length 4, where for any two strings s and t in A, sRt if s and t have the same first two characters. The question is whether the order of the first two characters matters in determining the relation.
  • #1
wolfmanzak
26
0

Homework Statement


Let A be the set of all strings of a's and b's of length 4. Define a relation R on A as follows. For all s,t [tex]\in A, sRt,[/tex] s has the same first two characters as t.

s=baaa
t=abaa

Homework Equations


The Attempt at a Solution



I just want to know if the order of the first two characters matters? if it does then they are not related, if it does not, they they are related.
 
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  • #2
What is the exact statement of the problem? I would be inclined to interpret "has the same first two characters" as meaning that order is not relevant- but then I'm not grading you!
 
  • #3
Unfortunately that is the exact way the problem is written which is why I'm also a bit confused. I'm inclined to agree with you on the belief that order doesn't matter, but I wasn't entirely sure. I've tried finding a good example or a source of info on the internet but have yet to find one. Any thoughts?

Thanks,
WMZ
 

FAQ: Discrete Structures Question on a Relation

What is a relation in discrete structures?

A relation in discrete structures is a mathematical concept that describes the connection or association between two sets of elements. It is represented as a set of ordered pairs where the first element is from one set called the domain and the second element is from another set called the range. In simpler terms, it is a way to relate or compare elements from two different sets.

What are the different types of relations in discrete structures?

There are several types of relations in discrete structures, including reflexive, symmetric, transitive, and antisymmetric relations. A reflexive relation is one where every element in the domain is related to itself. A symmetric relation is one where if x is related to y, then y is also related to x. A transitive relation is one where if x is related to y and y is related to z, then x is also related to z. An antisymmetric relation is one where if x is related to y and y is related to x, then x and y must be the same element.

How is a relation represented?

A relation can be represented in several ways, including as a table, a graph, or a matrix. In a table representation, the ordered pairs are listed in rows and columns. In a graph representation, the elements from one set are plotted on the x-axis and the elements from the other set are plotted on the y-axis. In a matrix representation, the rows represent the elements from one set and the columns represent the elements from the other set, with the cells indicating whether the elements are related or not.

What is the difference between a function and a relation?

A function is a special type of relation where each element from the domain is related to exactly one element in the range. In other words, there are no repeated inputs in a function. On the other hand, a relation can have repeated inputs and still be considered a valid relation. Additionally, a function must pass the vertical line test, meaning that a vertical line cannot intersect the graph of a function more than once.

How are relations used in real-life applications?

Relations have many real-life applications, such as in database management systems, social networks, and computer algorithms. In databases, relations are used to organize and categorize data, making it easier to search and retrieve information. In social networks, relations are used to connect individuals and establish connections between them. In computer algorithms, relations are used to solve problems and make decisions based on the connections between different elements.

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