[Math] Relations: Reflexive, symmetric, transitive

Question

I am having difficulties determining if this relation is reflexive, symmetric, transitive, or none of these.

Let A be the set of all strings of $0's$, $1's$, and $2's$ of length $4$. Define a relation $R$ on $A$ as follows: For all $s$, $t ∈ A$, $s$ R $t$ if and only if the sum of the characters in s equals the sum of the characters in t.

Examples this is true:

$0121$ R $2200$

$1220$ R $2111$

Answer 1

Tip: Any relation that is defined like $aRb$ iff $f(a)=f(b)$ for some function $f$ is an equivalence. Try if you can prove that.

Protip: The converse also holds by passing to the quotient.