Proposition 5.5. Assuming that:

• ${(A_j)}_{j\in J}$, $U$, $\sim$ as usual.

• $B_j,C_j\subseteq A_j$

• (1) $[{(B_j)}_{j\in J}]\cap [{(C_j)}_{j\in J}]=[{(B_j\cap C_j)}_{j\in J}]$.
• (2) $[{(B_j)}_{j\in J}]\cup [{(C_j)}_{j\in J}]=[{(B_j\cup C_j)}_{j\in J}]$.
• (3) $[{(B_j)}_{j\in J}]\setminus [{(C_j)}_{j\in J}]=[{(B_j\setminus C_j)}_{j\in J}]$.