Step-by-step Solution:

Statement A: \[ A - (B \cap C) = (A \cap B) - (A \cap C) \] Expanding the left-hand side: \[ A - (B \cap C) = A \cap (B \cap C)^c \] Using De Morgan’s law: \[ (B \cap C)^c = B^c \cup C^c \] So, \[ A \cap (B^c \cup C^c) = (A \cap B^c) \cup (A \cap C^c) \] which does not match the right-hand side.
Thus, Statement A is incorrect.
Statement B: \[ A - (B \cup C) = (A - B) \cap (A - C) \] Expanding both sides: \[ A - (B \cup C) = A \cap (B \cup C)^c \] Using De Morgan’s law: \[ (B \cup C)^c = B^c \cap C^c \] So, \[ A \cap (B^c \cap C^c) = (A \cap B^c) \cap (A \cap C^c) \] Since: \[ A - B = A \cap B^c, \quad A - C = A \cap C^c \] We get: \[ (A - B) \cap (A - C) = (A \cap B^c) \cap (A \cap C^c) \] which matches the left-hand side, so Statement B is correct.
Statement C: \[ n(A - B) = n(A) - n(A \cap B) \] From set theory, the number of elements in \( A - B \) is: \[ n(A - B) = n(A \cap B^c) \] Since: \[ n(A) = n(A \cap B) + n(A \cap B^c) \] Rearranging: \[ n(A \cap B^c) = n(A) - n(A \cap B) \] which confirms Statement C is correct.
Statement D: \[ A \cap (B - C) = (A \cap B) \cap (A - C) \] Expanding the left-hand side: \[ B - C = B \cap C^c \] So: \[ A \cap (B - C) = A \cap (B \cap C^c) \] Rearrange: \[ (A \cap B) \cap C^c \] Since: \[ A - C = A \cap C^c \] We get: \[ (A \cap B) \cap (A - C) \] which confirms Statement D is correct.
Final Answer:
A is incorrect.
B, C, and D are correct.