Concept guide
Subset: proving inclusion from an arbitrary element and refuting it by a counterexample
In the universe ℤ, let A be the set of multiples of 6, B the set of even integers and C the set of multiples of 4. Prove A⊆B and that this inclusion is strict (A≠B); prove A⊄C even though A and C share the element 12; note that B⊆B holds (⊆ allows equality); and prove {6}⊆A ⇔ 6∈A while separating the type roles of the two statements.