• Sep 13th 2009, 09:13 AM
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.
• Sep 13th 2009, 09:16 AM
Plato
Quote:

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?
• Sep 13th 2009, 09:23 AM
abc512
A and B are sets. R[A] means the binary relation of A.
• Sep 13th 2009, 10:06 AM
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.
• Sep 13th 2009, 10:11 AM
spaceship42
Quote:

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?
• Sep 13th 2009, 10:23 AM
Plato
Quote:

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?