Q.Let $U = \{1, 2, 3, \dots, 10\}$, $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7, 8\}$. Find $A \cup B$, $A \cap B$, $A - B$, $B - A$, $A'$, and verify that $(A \cup B)' = A' \cap B'$.

[!TLDR] Compute union, intersection, both differences and the complement, then check De Morgan's law. [!ANSWER] $A \cup B=\{1,2,3,4,5,6,7,8\}$, $A \cap B=\{4,5\}$, $A-B={1,2, …

With $U=\{1,\dots,10\}$, $A=\{1,2,3,4,5\}$, $B=\{4,5,6,7,8\}$: $A \cup B = \{1,2,3,4,5,6,7,8\}$ (every element in at least one set); $A \cap B = \{4,5\}$ (common to both); $A - B = \{1,2,3\}$ (in $A$, not in $B$); $B - A = \{6,7,8\}$ (in $B$, not in $A$); $A' = U - A = \{6,7,8,9,10\}$. Also $B' = U - B = \{1,2,3,9,10\}$. Now $(A \cup B)' = U - \{1,\dots,8\} = \{9,10\}$ …

Compute each operation directly from the element lists of $A$, $B$ and $U$, then compar …

A common error is computing $A'$ or $B'$ with respect to the wrong universal set, or forgetting that $ …