Question

Hi, I am just troubled to read the notation. (About sets and their relations.)

Answer 1

Suppose I have sets A and B.

What does \(\displaystyle A\circ B\) means?

Answer 2

(It would be really cool if someone can explain what that means, and give me an example of how to perform this operation. Thank you.)

Answer 3

Is that sort of like f o g? Because I think I can explain that fairly well.

Answer 4

It's possible that the intent is "some operation" on the two sets.
If we're talking about the relations, and not just the sets, it is likely the composition of two relations.
There may be other uses of the notation. Not all notations mean the same thing to every author. Please provide greater context.

Answer 5

I am provided a few sets
A, B and C.

And then asked to answer the "following questions concerning the relations above".
Suppose I have sets A and B.

\(\displaystyle A\circ B\)
\(\displaystyle B\circ A\)
\(\displaystyle B^{-1}\circ A\)
\(\displaystyle{\rm Dom}(C)~~~{\rm and}~~~{\rm Rng}(C)\)

Answer 6

A = {(2,4), (3,1), (3,4), (5,5)}
B = {(1,5), (2,2), (3,2), (3,4), (5,2)}
C = \(\left\{(x,y)\in \mathbb{R}\times\mathbb{R}:~~y=1/(x-1)\right\}\)

Answer 7

That is the full context/content of the problem.

Answer 8

Fair enough. The set IS the collection of individual mappings. Clearly, I think, this means the composition of the relations.

A∘B means to 1st map through the relation described by A and subsequently map the result through the relation described by B.

Answer 9

A little more than a little confused as regards to the last comment. (Sorry)

Answer 10

^ I think it's the opposite of that isn't it?
It's the mapping of B, that is then put through A.

Example:
B maps the x-coordinate 5 to 2.
Then A maps the x-coordinate 2 to 4.

So A∘B would contain (5,4)

Answer 11

Fair enough. Some authors do it the other way. You'll have to consult your text for that. The notation is NOT consistent throughout very many decades.

Answer 12

Fair enough :)

Answer 13

Fairly unfair enough that these stupid mathematicians (not you guys) could not even come to consent about notations.

Answer 14

Thank you guys, anyway ...

Answer 15

Bye