The set $A = \{1,2,3,4,5,6\}$ is given. Write one equivalence relation from this set, write the equivalence classes and write the elements of the quotient set, and in the end on the set $B = \{1,2,3,4\}$ write the equivalence relation that has binomial ($2$-member) quotient set.
For the first part of the problem involving set A, the equivalence relation I wrote is:
\begin{gather}\{(1,1),(2,2),(3,3),(4,4),(5,5),\\(6,6),(1,2),(2,1),(2,3),(3,2),(3,5),(5,3)(3,6),(6,3)\}\end{gather}
Is my equivalence relation correct ?
Equivalence classes:
$$ [1] = \{1,2\} , [2] = \{2,1,3\} , [3] = \{3,2,5\} , [4] = \{4\},
[5] = \{5,3\} , [6] = \{6,3\}$$
Are they correct?
Elements of the quotient set : ??
Could you help me with this one ?
Second part of the problem involving set B, I don't know how to solve so could you help me with this one as well ?