I am tasked to show each equivalence class in $\{0,1\}^4$ (means every $4$ bit string made with $0$ and $1$).
We know that they are $2^4 = 16$ different strings you can have.
I thought that for that each equivalence class is defined by having n number 1s in their string. i.e: all strings with one $1$ together, etc...
So looking up the solution we have: $\{0000\} \{0001, 0010, 0100, 1000\} \{0011, 0110, 1100, 1001\} \{0101, 1010\} \{0111,1011,1101,1110\} \{1111\}$.
Why does the equivalence class $\{0101,1010\}$ exists? Why it's not in $\{0011, 0110, 1100, 1001\}$ ?