Subset – Python

Subset and Superset are two fundamental concepts in set theory. Python also has built-in methods to support these concepts.

Subsets

A set is defined as the subset of another set, if first set all elements are also elements of second set. i.e. set A will be the subset of set B if all elements of set A are also elements of set B.

Subset – Mathematical Definition

Subset is denoted with symbol ⊆. Above definition can be denoted as A ⊆ B. If set A is a subset of set B, then it means that set A and set B are either equal OR all elements of set A are also elements of set B.

In Mathematics, subset can be defined as A ⊆ B ⟺ ∀ x ( x ∈ A ⟹ x ∈ B ). Lets understand this with an example:

Subset symbol ⊆ also includes equality in it. This leads to the concept of Proper Subset.

Proper Subset: set A is a proper subset of set B, if A ⊆ B and A ≠ B. This is denoted as A ⊂ B. Example – A = {10, 20} and B = {10, 20, 30}. Here, A ⊂ B because set A is contained within set B and A ≠ B.

Properties of Subsets

• Reflexivity: Every set is always a subset of itself, A ⊆ A.
• Transitivity: If A ⊆ B and B ⊆ C, then A ⊆ C. It means, if set A is a subset of set B and set B is a subset of set C, then it make set A subset of Set C also. Example – A = {10, 20}, B = {10, 20, 30}, C = {10, 20, 30, 40}
• Antisymmetry: If A ⊆ B and B ⊆ A, then A = B. It means, if set A is a subset of set B and set B is a subset of set A, then both set A and set B should be equal. Example – A = {10, 20}, B = {10, 20}

Python provides built-in method issubset() to check if the set is subset to another set or not. Lets see, how issubset() method works in Python.

Using issubset() method

• Syntax – set_1.issubset(set_2)
• issubset() method takes a single “iterable” as an argument.
• set_1.issubset(set_2) method returns boolean (True or False) value. True means set_1 is a subset of set_2 and False means set_1 is not a subset of set_2.

# using issubset() method
print("using issubset() method")
set_1 = {10, 20, 30}
set_2 = {10, 20, 30, 70, 80, 90}

subset_set12 = set_1.issubset(set_2)      # check set_1 is subset of set_2
subset_set21 = set_2.issubset(set_1)      # check set_2 is subset of set_1

print(set_1)
print(set_2)
print(subset_set12)     # return value for set_1 is subset of set_2
print(subset_set21)     # return value for set_2 is subset of set_1

We have defined two sets referenced by variables set_1 and set_2. Using built-in issubset() method we are checking if set_1 and set_2 are subset to each other or not. Output from issubset() method will be a boolean value.

Program Output

using issubset() method
{10, 20, 30}                         # elements of set_1
{80, 20, 90, 70, 10, 30}      # elements of set_2
True                 # set_1 is subset of set_2
False               # set_2 is subset of set_1

From the program output, set_1 and set_2 elements are printed. issubset() method has return a boolean (True or False) value. True for set_1 is subset of set_2 and False when set_2 is not subset of set_1.

Using issubset() method – with empty sets

• Syntax – set_1.issubset(set_2)

# using issubset() method - with empty set
print("using issubset() method - with empty set")
set_1 = set()
set_2 = set()

subset_set12 = set_1.issubset(set_2)          # check set_1 is subset of set_2
subset_set21 = set_2.issubset(set_1)          # check set_2 is subset of set_1
print(set_1)
print(set_2)
print(subset_set12)     # will return True = set_1 is subset of set_2
print(subset_set21)     # will return True = set_2 is subset of set_1

We have defined two sets referenced by variables set_1 and set_2. Both sets are empty sets. Using built-in issubset() method we are checking if set_1 is subset of set_2 OR set_2 is subset of set_1. Output from issubset() method will be a boolean value.

Program Output

using issubset() method - with empty set
set()                # elements of set_1
set()                # elements of set_2
True                # set_1 is subset of set_2
True                # set_2 is subset of set_1

Since both set_1 and set_2 are empty sets, so they are subset to each other. As an output we got True for both set_1 subset of set_2 and set_2 subset of set_1.

Using subset (<=) operator

• Syntax – set_1 <= set_2
• set_1 <= set_2 returns boolean (True or False) value. True means set_1 is a subset of set_2 and False means set_1 is not a subset of set_2.

# using subset (<=) operator
print("using subset (<=) operator")
set_1 = {10, 20, 30}
set_2 = {10, 20, 30, 70, 80, 90}

subset_set12 = set_1 <= set_2             # check set_1 is subset of set_2
subset_set21 = set_2 <= set_1             # check set_2 is subset of set_1

print(set_1)
print(set_2)
print(subset_set12)          # will return True = set_1 is subset of set_2
print(subset_set21)          # will return False = set_2 is not subset of set_1

We have defined two sets referenced by variables set_1 and set_2. Using subset (<=) operator, we are checking if set_1 and set_2 are subset to each other or not. Output from subset (<=) operator will be a boolean value.

Program Output

using subset (<=) operator
{10, 20, 30}                         # elements of set_1
{80, 20, 90, 70, 10, 30}      # elements of set_2
True                 # set_1 is subset of set_2
False               # set_2 is subset of set_1

From the program output, set_1 and set_2 elements are printed. subset (<=) operator has return a boolean (True or False) value. True for set_1 is subset of set_2 and False for set_2 is subset of set_1.

Using proper (strict) subset (<) operator

• Syntax – set_1 < set_2 (Note – we have only less than operator, equal to sign is not with it)
• set_1 < set_2 returns boolean (True or False) value. True means set_1 is a subset of set_2 and False means set_1 is not a subset of set_2.
• This operator is useful to check if set_1 is proper subset of set_2 or not.

# using strict subset (<) operator
print("using strict subset (<=) operator")
set_1 = {10, 20, 30}
set_2 = {10, 20, 30, 70, 80, 90}

subset_set12 = set_1 < set_2             # check set_1 is proper subset of set_2
subset_set21 = set_2 < set_1             # check set_2 is proper subset of set_1

print(set_1)
print(set_2)
print(subset_set12)          # will return True = set_1 is subset of set_2
print(subset_set21)          # will return False = set_2 is not subset of set_1

We have defined two sets referenced by variables set_1 and set_2. Using proper (strict) subset (<) operator, we are checking if set_1 and set_2 are proper subset to each other or not. Output from proper (strict) subset (<) operator will be a boolean value.

Program Output

using strict subset (<=) operator
{10, 20, 30}                         # elements of set_1
{80, 20, 90, 70, 10, 30}      # elements of set_2
True                 # set_1 is subset of set_2
False               # set_2 is subset of set_1

From the program output, set_1 and set_2 elements are printed. Proper (strict) subset (<) operator has return a boolean (True or False) value. True for set_1 is proper subset of set_2 and False shows that set_2 is not proper subset of set_1.

Custom implementation – issubset() method

Internally in Python, issubset() method checks for all elements of set_1 are present in set_2. If any element of set_1 is not present in set_2, then method returns False; otherwise, it returns True.

Lets see the custom code to implement functioning of issubset() method.

def custom_issubset(set_1, set_2):
    # Iterate through elements of set_1
    for element in set_1:
        # Check if any element of set_1 not in set_2
        if element not in set_2:
            return False
    return True

set_1 = {10, 20, 30}
set_2 = {10, 20, 30, 40, 50, 60}
set_3 = set()         # check for empty sets
set_4 = set()         # check for empty sets

print(custom_issubset(set_1, set_2))  # Output: True
print(custom_issubset(set_2, set_1))  # Output: False
print(custom_issubset(set_3, set_4))  # Output: True, check for empty sets

• custom_issubset() function iterates through each element in set_1.
• For each element in set_1, it checks if the element is present in set_2 or not.
• If any element is not found in set_2, the function returns False, else it will continue to check for all the elements of set_1. If all elements of set_1 are present in set_2, then it will return True.

Summary

In this article we learn about various subset operation on Sets. Following scenarios were explored:

• Subset – Mathematical Definition
• Using issubset() method
• Using issubset() method – with empty sets
• Using subset (<=) operator
• Using proper (strict) subset (<) operator
• Custom implementation – issubset() method

Code – Github Repository

All code snippets and programs for this article and for Python tutorial, can be accessed from Github repository – Comments and Docstring in Python.

Interview Questions & Answers

Q: What happens when we use issubset() with a non-set type, like a list or a dictionary?

issubset() method can be used with other iterables like lists or dictionaries.

• With lists, it checks if all elements of the set are present in the list.
• With dictionaries it checks if all elements of the set are present as the dictionary keys.

set_1 = {10, 20, 30}
list_1 = [10, 20, 30, 40]

print(set_1.issubset(list_1))         # True

dict_1 = {10: 'Python', 20: 'Power BI', 30: 'LLM'}
print(set_1.issubset(dict_1))         # True

Q: What is the time complexity of the issubset() method?

Time complexity of issubset() method is O(len(set_1)) where set_1 is the set being checked for subset of another set or iterable. Python iterate over all elements of set set_1 and check if each element is present in another set. Since, sets are implemented as hash sets, time complexity to check membership is O(1).

Q: Provide a real-world example where issubset() method can be used?

Consider a scenario where you have a list of skills required for a job and a list of skills a candidate possesses. You want to check if the candidate is qualified for the job by ensuring that all required skills are present in the candidate’s skill set.

Q: What are the common mistakes when using the issubset() method?

• Confuse with other methods – Developers might confuse issubset() with other set operations like issuperset(), which checks the superset condition, which is opposite to subset condition.
• Type of iterables – issubset() can work with other iterables like lists, it’s important to understand how Python interprets this. For instance, using issubset() on a dictionary will only consider the keys, not the values.
• Mutable elements in sets – Sets in Python cannot contain mutable elements like lists. Using issubset() with a set containing such elements will raise an error.