1. ## Question about Binary relations

I'm working on binary relation questions and I think I'm just confused about what exactly it means to be a binary relation. One of the questions is

$\displaystyle R[A- B] \supseteq R[A] - R[b]$ and I'm supposed to show that the superset can't be replaced by an equal sign.

All of the B's should be capitalized.

2. Originally Posted by abc512
I'm working on binary relation questions and I think I'm just confused about what exactly it means to be a binary relation. One of the questions is

$\displaystyle R[A- B] \supseteq R[A] - R[b]$ and I'm supposed to show that the superset can't be replaced by an equal sign.

All of the B's should be capitalized.
What are A & B?
What does R[A] mean?

3. A and B are sets. R[A] means the binary relation of A.

4. Are you sure it is not $\displaystyle R[A- B] {\color{red}\subseteq} R[A] - R[b]$?
If not then I do not understand the question.
Because I can give you a counter example to the way you have written it.

5. Originally Posted by Plato
Are you sure it is not $\displaystyle R[A- B] {\color{red}\subseteq} R[A] - R[b]$?
If not then I do not understand the question.
Because I can give you a counter example to the way you have written it.
No, it's definitely the $\displaystyle \supseteq$ . Another problem I have is
$\displaystyle R[A \cap B] \subseteq R[A] \cap R[b]$ and to show that $\displaystyle \subseteq$ can be replaced by =. Would you be able to explain that one better?

6. Originally Posted by spaceship42
No, it's definitely the $\displaystyle \supseteq$ . Another problem I have is
$\displaystyle R[A \cap B] \subseteq R[A] \cap R[b]$ and to show that $\displaystyle \subseteq$ can be replaced by =. Would you be able to explain that one better?
OK Look at this example. On $\displaystyle \{1,2,3,4,5,6,7,8\}$
define $\displaystyle R$ as $\displaystyle xRy$ if and only if $\displaystyle x|y$ (x divides y).
Now if $\displaystyle A=\{2,4,6,8\}~\&~B=\{1,2,3,4\}$ then $\displaystyle R[A\backslash B] \subset R[A]\backslash R[ B ]$.
But $\displaystyle R[A]\backslash R[ B ] \not\subseteq R[A\backslash B]$

So what am I not understanding about the question?