I'm working on these questions and I'm very confused about the difference between membership and inclusion.
If $a\in P(A∩B)\setminus C $ then:
- $(a\in D\setminus C)$ where $D = P(A \cap B)$;
- $a\subset (A \cap B)$ AND $(a \not\subset C)$;
- $a\subset(A \cap B)$ AND $(a \notin C)$;
- $a\subset A$ AND $a\subset B$.
Is the membership valid only between an element and a set or no? And in the inclusion valid only between sets? I searched a lot to do this exercise but i don't understand