BCA PART A 1.R program to implement operations of set (union, intersection, difference, subset).

 

Explanation

1. Union: The union() function combines all elements from both sets, removing duplicates.
2. Intersection: The intersect() function finds the common elements between the two sets.
3. Difference: The setdiff() function finds elements in one set that are not in the other.
   • setdiff(set_A, set_B) finds elements in set_A that are not in set_B.
   • setdiff(set_B, set_A) finds elements in set_B that are not in set_A.
4. Subset:
   • The expression all(set_A %in% set_B) checks if all elements of set_A are in set_B, indicating that set_A is a subset of set_B.
   • The expression all(set_B %in% set_A) checks if all elements of set_B are in set_A, indicating that set_B is a subset of set_A.
   • A proper subset is determined by checking if one set is a subset of the other but not vice versa.

Program

# Define two sets as vectors
set_A <- c(1, 2, 3, 4, 5)
set_B <- c(4, 5, 6, 7, 8)

# Union of sets
union_set <- union(set_A, set_B)
cat("Union of set_A and set_B:\n")
print(union_set)

# Intersection of sets
intersection_set <- intersect(set_A, set_B)
cat("\nIntersection of set_A and set_B:\n")
print(intersection_set)

# Difference of sets (set_A - set_B)
difference_set_A_B <- setdiff(set_A, set_B)
cat("\nDifference of set_A - set_B:\n")
print(difference_set_A_B)

# Difference of sets (set_B - set_A)
difference_set_B_A <- setdiff(set_B, set_A)
cat("\nDifference of set_B - set_A:\n")
print(difference_set_B_A)

# Check if set_A is a subset of set_B
is_subset_A_B <- all(set_A %in% set_B)
cat("\nIs set_A a subset of set_B?:\n")
print(is_subset_A_B)

# Check if set_B is a subset of set_A
is_subset_B_A <- all(set_B %in% set_A)
cat("\nIs set_B a subset of set_A?:\n")
print(is_subset_B_A)

# Check if a set is a proper subset
is_proper_subset_A_B <- all(set_A %in% set_B) && !all(set_B %in% set_A)
cat("\nIs set_A a proper subset of set_B?:\n")
print(is_proper_subset_A_B)

Output :

Union of set_A and set_B:

[1] 1 2 3 4 5 6 7 8

Intersection of set_A and set_B:

[1] 4 5

Difference of set_A - set_B:

[1] 1 2 3

Difference of set_B - set_A:

[1] 6 7 8

Is set_A a subset of set_B?:

[1] FALSE

Is set_B a subset of set_A?:

[1] FALSE

Is set_A a proper subset of set_B?:

[1] FALSE

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