# Thread: What is the relation?

1. ## What is the relation?

Hi there,
Can someone give me a push in the right direction?

I have this assignment I have to make, I study beta gamma with math as a major.
This is the question:
A is a non empty set, and X1 and X2 are equivalence relations on A. X is also an equivalence relation on A, because X = the set of the element that are X1 and X2.
T1 is the partition of A that corresponds to X1, and T2 is the partition of A that corresponds to X2. T is the partition that corresponds to X.
The question: What is the relation between T1, T2 and T?

I also have to prove it, but I think I can do that myself...if I know which way to go.

Mary

2. Originally Posted by MaryB
This is the question:
A is a non empty set, and X1 and X2 are equivalence relations on A. X is also an equivalence relation on A, because X = the set of the element that are X1 and X2. T1 is the partition of A that corresponds to X1, and T2 is the partition of A that corresponds to X2. T is the partition that corresponds to X.
The question: What is the relation between T1, T2 and T?
Anyone majoring in mathematics needs to practice being clear in writing mathematics.
As I understand it $\displaystyle X=X_1\cap X_2$ which is non-empty because $\displaystyle \Delta_A\subseteq X_1\cap X_2$.
The respective partitions are $\displaystyle T_1,~T_2~\&~T$.

I think this is what the question means.
$\displaystyle C \in T \Leftrightarrow \left( {\exists C_1 \in T_1 } \right)\left( {\exists C_2 \in T_2 } \right)\left[ {C = C_1 \cap C_2 } \right]$

3. Originally Posted by Plato
Anyone majoring in mathematics needs to practice being clear in writing mathematics.
I don't really know what you mean by that, but if you mean that my question is'nt crystal clear, well...it's literally taken from the assignments I got from my teacher. I can't make it any clearer than it is on copy's

tnx for your explanations!