I'm rather new to higher math problems including proofs etc. I've now got a problem in front of me which I cannot wrap my head around on how to approach it:
$(a,b)$ can be defined as the subset $\{\{a\}, \{a, b\}\} \subseteq P(A \cup B)$.
Show:
For $a, a' \in A$ and $b, b' \in B$ holds:
$(a, b) = (a', b') \leftrightarrow a = a'$ and $b = b'$
I simply don't even really know where to start here. Do you have any tips/ resources on how to apporach these kind of problems?