Let A and B be subsets of the finite universal set U. Show that

SolutionStep 1Let us assume that A and B are the subsets of the finite universal set U.Use the De Morgan’s Law|| = || || = ||Use the properties of Universal SetU = || + |A B| || = |U| - |A B|Now, Use the Principle of Exclusion and Inclusion|A B| = |A| + |B| - |AB| || = |U| - (|A| + |B| - |AB|) = |U| - |A| - |B| + |AB|Hence, it is proved that || = |U| - |A| - |B| + |AB|