Looking for a Book on Sets, Groups, and Relations with Exercises?

In summary, sets are collections of distinct elements and groups are sets with additional defined operations. Relations show connections between elements of sets and groups, and are used in various branches of mathematics. Real-life applications of these concepts can be found in computer science, such as data structures and encryption algorithms. Common properties of sets, groups, and relations include closure, associativity, and identity elements.
  • #1
dsfranca
23
0
Hi,
I would like to know if you guys know a good book on sets groups and relations, preferably with lots of exercises. I believe that I am on a beginner level, but I already know all basic concepts, so the text is not that important. It would be even better if it is available online hehe!
Thks!
 
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  • #3
Thks, I will take a look at it!
 

FAQ: Looking for a Book on Sets, Groups, and Relations with Exercises?

What is the difference between a set and a group?

A set is a collection of distinct elements, while a group is a set with an additional operation defined on it that satisfies certain properties, such as closure, associativity, and inverse elements.

What is a relation and how is it related to sets and groups?

A relation is a set of ordered pairs that show the connection between elements of two sets. It can be defined on both sets and groups, and can help establish connections and patterns between elements.

How are sets, groups, and relations used in mathematics?

Sets, groups, and relations are fundamental concepts in mathematics that are used to define and study abstract structures and relationships between objects. They have applications in various branches of mathematics, such as algebra, topology, and calculus.

Can you give an example of a real-life application of sets, groups, or relations?

One example could be in computer science, where sets and groups are used to represent data structures and group operations are used in encryption algorithms. Relations can also be used to model social networks or decision-making processes.

What are some common properties of sets, groups, and relations?

Some common properties include closure, associativity, and commutativity. Sets and groups also have identity and inverse elements, while relations can have properties such as reflexivity, symmetry, and transitivity.

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