Question 1171361
Let $U = \{a, b, c, d, e, f, g, h, i, j\}$, $A = \{a, b, c, d, e\}$, $B = \{a, b, d, f, g\}$, and $C = \{a, d, e\}$.

1.  **(A ⊕ C) \ B**

    * $A \oplus C = (A \setminus C) \cup (C \setminus A)$
    * $A \setminus C = \{b, c\}$
    * $C \setminus A = \emptyset$
    * $A \oplus C = \{b, c\} \cup \emptyset = \{b, c\}$
    * $(A \oplus C) \setminus B = \{b, c\} \setminus \{a, b, d, f, g\} = \{c\}$

2.  **(A \ C) ∩ (B \ C)**

    * $A \setminus C = \{b, c\}$
    * $B \setminus C = \{b, f, g\}$
    * $(A \setminus C) \cap (B \setminus C) = \{b, c\} \cap \{b, f, g\} = \{b\}$

3.  **n(A<sup>c</sup> ∪ B<sup>c</sup>)**

    * $A^c = U \setminus A = \{f, g, h, i, j\}$
    * $B^c = U \setminus B = \{c, e, h, i, j\}$
    * $A^c \cup B^c = \{c, e, f, g, h, i, j\}$
    * $n(A^c \cup B^c) = |A^c \cup B^c| = 7$

Therefore:

* (A ⊕ C) \ B = {c}
* (A \ C) ∩ (B \ C) = {b}
* n(A<sup>c</sup> ∪ B<sup>c</sup>) = 7