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

Understand the definitions of subset and superset

A set A is a subset of another set B if every element in A is also an element of B. The notation A ⊆ B is used to denote that A is a subset of B. Similarly, a set B is a superset of another set A if every element in A is also an element of B. The notation B ⊇ A is used to denote that B is a superset of A.

Examine the given sets

We have two sets: - set1 = {1, 2, 3, 4} - set2 = {2, 3}

Check for subset and superset relations

Since all elements in set2 (2 and 3) are included in set1, we can say that set2 is a subset of set1. Using the notation, set2 ⊆ set1. As set1 contains all elements of set2 and more, set1 is a superset of set2. Using the notation, set1 ⊇ set2. In conclusion, set2 is a subset of set1, and set1 is a superset of set2.

Key concepts

Subset

Understanding subsets is a fundamental part of working with Python sets. When we say that a set \( A \) is a subset of set \( B \), this means that every element in \( A \) is also found in \( B \). The subset relationship is indicated by the symbol \( \subseteq \). This doesn't necessarily mean that \( B \) cannot have more elements outside of \( A \), only that nothing in \( A \) is missing from \( B \). In Python, you can check if a set is a subset using the built-in method `issubset()`. For example:

• `set2.issubset(set1)` will return True if set2 is a subset of set1.

In the exercise, we determined that \( \{2, 3\} \subseteq \{1, 2, 3, 4\} \). This tells us every element of \( set2 \) is in \( set1 \), confirming the subset relationship.

Superset

A superset is simply the opposite concept of a subset. Set \( B \) is a superset of set \( A \) if it contains all elements of \( A \). The notation \( \supseteq \) is used to show this relationship. Essentially, this means that \( A \subseteq B \) is the same as saying \( B \supseteq A \). In Python, we can use the `issuperset()` method to check for supersets. For instance:

• `set1.issuperset(set2)` would yield True if set1 is a superset of set2.

In our example, \( set1 = \{1, 2, 3, 4\} \) is indeed a superset of \( set2 = \{2, 3\} \). This confirms that \( set1 \) includes every element of \( set2 \), and possibly more.

Set Operations

Set operations in Python allow us to perform mathematical-like operations between different sets. These include finding unions, intersections, differences, and symmetric differences, among others.

• Union: Combining all elements from both sets. Use the `union()` method or the `|` operator.
• Intersection: Finding common elements present in both sets. Use the `intersection()` method or the `&` operator.
• Difference: Elements present in one set but not in the other. Use the `difference()` method or the `-` operator.
• Symmetric Difference: Elements present in either of the sets but not in both. Use the `symmetric_difference()` method or the `^` operator.

These operations illustrate the versatility of Python sets. They are particularly helpful for tasks such as data analysis and managing collections of items. For example, determining common subscribers between two email lists or identifying exclusive features in one product version compared to another.