## Definition ==Set Operations== are the fundamental ways of combining or modifying sets: union ($A \cup B$, elements in $A$ or $B$ or both), intersection ($A \cap B$, elements in both $A$ and $B$), complement ($A^c$, elements not in $A$), and difference ($A \setminus B$, elements in $A$ but not in $B$). These operations translate directly into logical statements about events in probability. > [!example]- If $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cap B) = 0.2$, what is $P(A^c \cap B)$? > $A^c \cap B$ represents the part of $B$ that does not overlap with $A$. > $ P(A^c \cap B) = P(B) - P(A \cap B) = 0.5 - 0.2 = 0.3 $