Count number of Equivalence Relations
- Thread starter anirban
- Start date
Hello, anirban!
I don't understand the question,
but I will take a guess at what is expected here . . .
A relation is a connection between two elements of a set (not necessarily distinct).
It has the form: .\(\displaystyle x R y\), where \(\displaystyle x\) and \(\displaystyle y\) are elements of the set.
Hence, the question could be "How many different ordered pairs of elements can be made?"
In this example, there are 4 choices for the first element and 4 for the second.
. . Hence, there are: .\(\displaystyle 4^2 \,=\,16\) possible pairs.
\(\displaystyle \text{They are: }\;\begin{Bmatrix}1R1 & 1 R 2 & 1 R 3 & 1R4 \\ 2R1 & 2R2 & 2R3 & 2R4 \\ 3R1 & 3R2 & 3R3 & 3R4 \\ 4R1 &4R2 & 4R3 & 4R4 \end{Bmatrix}\)
How many of these are "equivalence relations"? . . . Who knows?
I don't understand the question,
but I will take a guess at what is expected here . . .
A relation is a connection between two elements of a set (not necessarily distinct).
It has the form: .\(\displaystyle x R y\), where \(\displaystyle x\) and \(\displaystyle y\) are elements of the set.
Hence, the question could be "How many different ordered pairs of elements can be made?"
In this example, there are 4 choices for the first element and 4 for the second.
. . Hence, there are: .\(\displaystyle 4^2 \,=\,16\) possible pairs.
\(\displaystyle \text{They are: }\;\begin{Bmatrix}1R1 & 1 R 2 & 1 R 3 & 1R4 \\ 2R1 & 2R2 & 2R3 & 2R4 \\ 3R1 & 3R2 & 3R3 & 3R4 \\ 4R1 &4R2 & 4R3 & 4R4 \end{Bmatrix}\)
How many of these are "equivalence relations"? . . . Who knows?
