I'm working on some problems involving set theory, more specifically subsets. I think I understand how it works, but just wanted to make sure that my thought process is correct.
For something to be a subset of something else all of the possible outputs of the set would need to be contained in set. For subsets to be equal they need have all of the exact same outputs, even if their inputs are different to get the outputs.
$A$ is a subset of $B$ because all possible outcomes of $A$ for any number plugged in equal a number that is in $B$
These sets are equal and also contained within each other because any output in $A$ can be found in $B$ with a different input. Am I thinking about these correctly?