If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, $A = \{1, 2, 3, 4\}$, $B = \{2, 4, 6, 8\}$, $C = \{3, 4, 5, 6\}$ find: (i) $A'$ (ii) $(A \cup C)'$ (iii) $(B - C)'$.

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> [!TLDR]
> Compute each set operation directly, then take the complement in $U=\{1,2,\dots,9\}$.
>
> Given $U=\{1,2,3,4,5,6,7,8,9\}$, $A=\{1,2,3,4\}$, $B=\{2,4,6,8\}$, $C=\{3,4,5,6\}$.
>
> **(i) $A'$:** $A' = U - A = \{5,6,7,8,9\}$ (all elements of $U$ not in $A$).
>
> **(ii) $(A\cup C)'$:** First, $A\cup C = \{1,2,3,4\}\cup\{3,4,5,6\} = \{1,2,3,4,5,6\}$.
> Then $(A\cup C)' = U - \{1,2,3,4,5,6\} = \{7,8,9\}$.
> …

Operation	What it asks	Bucket contains
Union ( $A \cup B$ )	In either?	Everything from $A$ or $B$ (or both)
Intersection ( $A \cap B$ )	In both?	Only the overlap
Difference ( $A \setminus B$ )	In $A$ but not $B$ ?	Just the part of $A$ that doesn't touch $B$
Complement ( $A^c$ )	Not in $A$ ?	Everything outside $A$ (inside $U$ )
Symmetric Difference ( $A \triangle B$ )	In exactly one?	The two crescent-shaped parts, excluding the overlap

Q.If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ , $A = \{1, 2, 3, 4\}$ , $B = \{2, 4, 6, 8\}$ , $C = \{3, 4, 5, 6\}$ find:

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Q.If U={1,2,3,4,5,6,7,8,9}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}U={1,2,3,4,5,6,7,8,9}, A={1,2,3,4}A = \{1, 2, 3, 4\}A={1,2,3,4}, B={2,4,6,8}B = \{2, 4, 6, 8\}B={2,4,6,8}, C={3,4,5,6}C = \{3, 4, 5, 6\}C={3,4,5,6} find:

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Q.If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ , $A = \{1, 2, 3, 4\}$ , $B = \{2, 4, 6, 8\}$ , $C = \{3, 4, 5, 6\}$ find:

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