Set Operations in R
Definition and Creation of Sets
In R, sets are often represented by vectors and manipulated using specialized functions. Although R does not have a native “set” type like some other languages, vectors can be used to represent sets and perform operations on them.
Creating Sets:
# Create sets A <- c(1, 2, 3, 4, 5) B <- c(4, 5, 6, 7, 8)
Basic Operations
Union
The union of two sets is a set containing all elements from both sets, with duplicates removed.
Function in R: union()
# Calculate the union union_set <- union(A, B) print(union_set) # [1] 1 2 3 4 5 6 7 8
Intersection
The intersection of two sets is a set containing only the elements present in both sets.
Function in R: intersect()
# Calculate the intersection intersection_set <- intersect(A, B) print(intersection_set) # [1] 4 5
Difference
The difference between two sets is a set containing the elements of the first set that are not in the second set.
Function in R: setdiff()
# Calculate the difference difference_set_A_B <- setdiff(A, B) print(difference_set_A_B) # [1] 1 2 3 difference_set_B_A <- setdiff(B, A) print(difference_set_B_A) # [1] 6 7 8
Symmetric Difference
The symmetric difference between two sets is a set containing elements that are in either of the sets but not in both.
Function in R: setxor()
# Calculate the symmetric difference symmetric_difference <- setxor(A, B) print(symmetric_difference) # [1] 1 2 3 6 7 8
Advanced Operations
Subset Check
Check if one set is a subset of another set.
Function in R: all() with match()
# Check if A is a subset of B is_subset <- all(A %in% B) print(is_subset) # [1] FALSE
Set Equality
Check if two sets are equal, meaning they contain the same elements.
Function in R: identical()
# Check if A and B are equal are_equal <- identical(sort(A), sort(B)) print(are_equal) # [1] FALSE
Manipulating Sets
Adding Elements
Add elements to a set by taking the union with a vector of new elements.
Example:
# Add elements to a set A <- union(A, c(9, 10)) print(A) # [1] 1 2 3 4 5 9 10
Removing Elements
Remove elements from a set by taking the difference.
Example:
# Remove elements from a set A <- setdiff(A, c(1, 10)) print(A) # [1] 2 3 4 5 9
Practical Applications
Example: Group Management
Suppose you manage groups of people and want to find members who are only in one group but not the other.
# Group memberships
group1 <- c("Alice", "Bob", "Charlie")
group2 <- c("Bob", "Charlie", "David")
# Members only in group1
only_group1 <- setdiff(group1, group2)
print(only_group1)
# [1] "Alice"
# Members only in group2
only_group2 <- setdiff(group2, group1)
print(only_group2)
# [1] "David"
Summary
- Union: union(A, B) — Combines all elements from both sets.
- Intersection: intersect(A, B) — Common elements between both sets.
- Difference: setdiff(A, B) — Elements in the first set but not in the second.
- Symmetric Difference: setxor(A, B) — Elements in either set but not in both.
- Subset Check: all(A %in% B) — Checks if all elements of A are in B.