Set Operations

Union: $A \cup B = \{\xi \mid \xi \in A \text{ or } \xi \in B\}$

Intersection $A \cap B = \{\xi \mid \xi \in A \text{ and } \xi \in B\}$

Complement: $A^c = \{\xi \mid \xi \in \Omega \text{ and } \xi \notin A\} = \Omega \setminus A$

Note the correspondence with logic: or, and, not

Difference: $A\setminus B = \{\xi \mid \xi \in A \text{ and } \xi \notin B\} = A \cap B^c$

A <- c(1,2,3,4,5)
B <- c(2,4,6)
union(A,B)

## [1] 1 2 3 4 5 6

intersect(A,B)

## [1] 2 4

setdiff(A,B)

## [1] 1 3 5