Question 1171361: Q1) Let U={a,b,c,d,e,f,g,h,i,j},A={a,b,c,d,e},B={a,b,d,f,g},C={a,d,e} Findl
(A⨁C)\B
(A\C)∩(B\C)
n(A^c∪B^c )
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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(Ac ∪ Bc)**
* $A^c = U \setminus A = \{f, g, h, i, j\}$
* $B^c = U \setminus B = \{c, e, h, i, j\}$
* $A^c \cup B^c = \{c, e, f, g, h, i, j\}$
* $n(A^c \cup B^c) = |A^c \cup B^c| = 7$
Therefore:
* (A ⊕ C) \ B = {c}
* (A \ C) ∩ (B \ C) = {b}
* n(Ac ∪ Bc) = 7
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