Q.If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify: (A∪B)' = (A'∩B)'.

$A \cup B = \{1,2,3,4\}\cup\{3,4,5,6\} = \{1,2,3,4,5,6\}$, so $(A\cup B)' = X - \{1,2,3,4,5,6\} = \{7,8,9,10\}$. Now $A' = X-A = \{5,6,7,8,9,10\}$ and $B' = X-B = \{1,2,7,8,9,10\}$, so $A'\cap B' = \{7,8,9,10\}$. Both equal {7,8,9,10}, confirming De Morgan's law $(A\cup B)' = A'\cap B'$ (the textbook's printed right side carries an extra, unintended p …

Find A∪B and complement it directly against the universal set X; separately complement A and B individually and interse …

Watch the source misprint: De Morgan's law is $(A\cup B)' = A' \cap B'$ with no extra prime on the right — an outer prime on $(A'\cap B')'$ …