The first picture represents the elements in B that are not (also) in A. So, we want the set difference of B and A:
[tex] B \setminus A = \{x \in B:\ x \notin A\} [/tex]
For the second picture, we can work like this: if we take all the elements belonging to A, we only need to add the bottom-right part, which is the intersection of B and C. So, we can express the blue part as
[tex] A \cup (B\cap C) = \{x:\ x \in A \lor (x\in B \land x\in C) \} [/tex]
