Set language and notation

Reading $\cap$ (∩, intersection — "in both A and B") as "or" and $\cup$ (∪, union — "A or B or both") as "and" (or simply swapping the symbols), so the wrong region is selected — e.g. giving the overlap when $A \cup B$ was asked for.

Picking Venn-diagram regions by eye rather than shading the set described and reading off only the shaded parts — this misfires for $A'$ (A′, the complement of A — everything in $\xi$ not in A), $A \cap B$ (∩ intersection — in both A and B) and $A \cup B$ (∪ union — A or B or both) alike.

$A'$ (A′, the complement of A — everything in $\xi$ (the universal set) not in A) means everything in the universal set $\xi$ that is not in $A$ — leaving out elements of $\xi$, or counting elements outside $\xi$, gives the wrong complement and the wrong $n(A')$.

Only $\subseteq$ allows equality: $\{2,4\} \subseteq \{2,4\}$ is true, but the proper subset $\{2,4\} \subset \{2,4\}$ is false. A subset sign sits between two SETS — to say one element belongs, use $\in$ (e.g. $4 \in A$), not $\subset$.

Each element appears once in a union, however many sets contain it. For $A=\{2,4,6\}$ and $B=\{4,6,8\}$ the union is $\{2,4,6,8\}$, not $\{2,4,6,4,6,8\}$. Repeating the overlap inflates the list and the value of $n(A \cup B)$.

$n(A)$ asks for the NUMBER of elements, not the elements themselves. If $A=\{3,6,9,12\}$ then $n(A)=4$, and the answer is the single number $4$ — not the set $\{3,6,9,12\}$. A "how many" question wants a count.