Encountered a question on set operations and am kind of lost...
$(D \bigcup \{A\})\oplus A$
$A: \{a,b,c,d\}, D: \{b,d\}$
Does $\{A\}$ mean $\{\{a,b,c,d\}\}$, making it a set of a set? Would set D union set of set A (?) be the same as set D union set A, or are they different?
I would understand how to list the elements if it were $(D \bigcup A)\oplus A$, but the $\{A\}$ is what is confusing me.
Good question!
However, you should write $$A = \{a,b,c,d\},D = \{b,d\},$$ because after all, $D$ is being defined to equal the set $\{b,d\}$, so why use a symbol other than the equality symbol to denote equality in this case?
You're correct that $\{A\}$ means $\{\{a,b,c,d\}\}$. Hence $$D \cup \{A\} = \{\{a,b,c,d\},b,d\},$$ which has three elements, assuming $b$ and $d$ are distinct. I'm sure you can take it from there.