Let $U = \{1, 2, \dots, 10\}$, $A = \{1,2,3,4,5\}$ and $B = \{4,5,6,7,8\}$. Find: (i) $A - B$ (ii) $B - A$ (iii) $A riangle B$ (iv) $A'$ and $B'$ (v) whether $A$ and $B$ are disjoint.

Question

Let $U = \{1, 2, \dots, 10\}$, $A = \{1,2,3,4,5\}$ and $B = \{4,5,6,7,8\}$. Find: (i) $A - B$ (ii) $B - A$ (iii) $A 	riangle B$ (iv) $A'$ and $B'$ (v) whether $A$ and $B$ are disjoint.

Accepted Answer

**(i) $A - B$:** elements in $A$ but not $B$. $A=\{1,2,3,4,5\}$; removing $4$ and $5$ (which are also in $B$) leaves $\{1,2,3\}$.

**(ii) $B - A$:** elements in $B$ but not $A$. $B=\{4,5,6,7,8\}$; removing $4$ and $5$ (also in $A$) leaves $\{6,7,8\}$.

**(iii) $A 	riangle B$:** combine $A-B$ and $B-A$: $\{1,2,3\} \cup \{6,7,8\} = \{1,2,3,6,7,8\}$ — the shared elements $4,5$ are deliberately excluded.

**(iv) Complements.** $A' = U - A = \{1,\dots,10\} - \{1,2,3,4,5\} = \{6,7,8,9,10\}$. $B' = U - B = \{1,\dots,10\} - \{4,5,6,7,8\} = \{1,2,3,9,10\}$. …

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.Let $U = \{1, 2, \dots, 10\}$ , $A = \{1,2,3,4,5\}$ and $B = \{4,5,6,7,8\}$ . Find:

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Q.Let U={1,2,…,10}U = \{1, 2, \dots, 10\}U={1,2,…,10}, A={1,2,3,4,5}A = \{1,2,3,4,5\}A={1,2,3,4,5} and B={4,5,6,7,8}B = \{4,5,6,7,8\}B={4,5,6,7,8}. Find:

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Q.Let $U = \{1, 2, \dots, 10\}$ , $A = \{1,2,3,4,5\}$ and $B = \{4,5,6,7,8\}$ . Find:

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