Set Operations in Programming: Union, Intersection, and Difference
How can we compute the specified set of operations for finite sets A and B in programming?
Assume that A and B are finite sets of integers. Write a subroutine in a programming language of your choice to compute the specified set of operations.
What are the elements of sets A and B that we need to work with?
Define two sets, A and B, with the following elements:
Set A: {1, 2, 3, 4, 5}
Set B: {3, 4, 5, 6, 7}
What are the specific set operations we need to compute?
Compute and print the union of sets A and B (GAUB).
Compute and print the intersection of sets A and B (A ∩ B).
Compute and print the difference of sets A and B (A - B).
Test your subroutines with these sets and display the results.
Solution:
To compute the specified set of operations for finite sets A and B, we can use a programming language like Python. Let's work with the given sets A and B to perform the required operations:
Set A: {1, 2, 3, 4, 5}
Set B: {3, 4, 5, 6, 7}
To calculate the union of sets A and B (GAUB), we need to find all the elements that are in either set A, set B, or both. This can be done with the following Python code:
```python def union(A, B): return list(set(A) | set(B)) A = [1, 2, 3, 4, 5] B = [3, 4, 5, 6, 7] print("Union of sets A and B (GAUB):", union(A, B)) ```To calculate the intersection of sets A and B (A ∩ B), we need to find the elements that are common to both sets. Here's the Python code for this operation:
```python def intersection(A, B): return list(set(A) & set(B)) A = [1, 2, 3, 4, 5] B = [3, 4, 5, 6, 7] print("Intersection of sets A and B (A ∩ B):", intersection(A, B)) ```For the difference of sets A and B (A - B), we need to find the elements in set A but not in set B. Here's how you can implement this in Python:
```python def difference(A, B): return list(set(A) - set(B)) A = [1, 2, 3, 4, 5] B = [3, 4, 5, 6, 7] print("Difference of sets A and B (A - B):", difference(A, B)) ```By running these Python code snippets, you can compute and display the results of the specified set operations for sets A and B.