Question

Look at the following code: set1 = set([1, 2, 3, 4]) set2 = set([2, 3]) Which of the sets is a subset of the other? Which of the sets is a superset of the other?

Short answer

Answer: Set2 is a subset of set1, and set1 is a superset of set2.

Step-by-step solution

Understanding subsets and supersets

A subset is a set that contains all its elements within another set, called the superset. If every element of set A is also an element of set B, then set A is a subset of set B, and set B is a superset of set A.

Analyzing the given sets

We are given two sets: set1 = {1, 2, 3, 4} set2 = {2, 3} Now, we need to compare the elements of these sets to determine the subset-superset relationship, if any.

Comparing elements of set1 and set2

By looking at the two sets, we can see that every element of set2 (2 and 3) is also an element of set1. This means that set2 is a subset of set1. And since set2 is a subset of set1, it follows that set1 is a superset of set2.

Conclusion

set2 is a subset of set1, and set1 is a superset of set2.

Key concepts

Python Sets

In Python, a set is a collection of unique elements that is both unordered and mutable. Unlike lists or tuples, sets cannot contain duplicate items, which makes them invaluable for tasks involving the elimination of duplicates from a sequence and for membership testing.

Creating a set can be done using curly braces {} or the set() constructor. For example, set1 = {1, 2, 3, 4} or set2 = set([2, 3]). The primary operations on sets include adding or removing items, testing for membership, and performing mathematical operations like unions, intersections, and differences.

When working with Python sets, understanding how they behave is crucial for programming related to data analysis, statistics, and other areas that require unique collections of elements.

Subset Comparison

The concept of a subset is foundational to set theory in mathematics, and it translates seamlessly into Python programming. A set 'A' is considered a subset of another set 'B' if all elements of 'A' are also elements of 'B'. In Python, a subset comparison can be performed with the issubset() method or the <= operator.

For example, using the sets from our exercise, we assess the relationship by set2.issubset(set1) or set2 <= set1, which returns True if 'set2' is indeed a subset of 'set1'. It is important to note that every set is considered a subset of itself in set theory, which is reflected in Python as well.

Superset Comparison

A superset is the flip side of a subset. A set 'B' is a superset of another set 'A' if 'B' contains all the elements of 'A'. This relationship is tested in Python using the issuperset() method or the >= operator. From our original example, we can verify that 'set1' is a superset of 'set2' by checking set1.issuperset(set2) or set1 >= set2, expecting True as the outcome.

Understanding superset relationships is helpful when we need to ensure that a set has a comprehensive collection of items, possibly derived from other sets. This is common when consolidating data from multiple sources or when deducing logical relationships within datasets.