Q.Verify De Morgan's law $(A \cup B)' = A' \cap B'$ for $U = \{1,2,\dots,10\}$, $A = \{1,2,3,4,5\}$ and $B = \{4,5,6,7\}$.

Compute the left side by first forming the union then complementing it; compute the right side by complementing each set first and then intersecting; check the two match.

Step 1 — Compute the LHS, $(A \cup B)'$. $A \cup B = \{1,2,3,4,5,6,7\}$ (combining both lists, counting the shared elements $4,5$ once). Its complement relative to $U = \{1,\dots,10\}$ is $(A\cup B)' = \{8,9,10\}$.

Step 2 — Compute the RHS, $A' \cap B'$. $A' = U - A = \{6,7,8,9,10\}$. $B' = U - B = \{1,2,3,8,9,10\}$. Their intersection (elements common to both) is $A' \cap B' = \{8,9,10\}$. …

A quick cardinality check: $n((A\cup B)')=10-7=3$ matches $n(A'\cap B')=3$, confirming both sides have the same …

Forgetting to take the complement relative to the STATED universal set $U$ — using a different or unstated un …