Question

After the following code executes, what elements will be members of set3? \\[\begin{array}{l}\text { set1 }=\operatorname{set}([1,2,3,4]) \\ \text { set2 }=\operatorname{set}([3,4,5,6]) \\\\\text { set } 3=\text { set } 2 \text { . difference (set1) } \end{array}\\]

Short answer

Answer: The elements of set3 are 5 and 6.

Step-by-step solution

Understand the given sets and operations

We are given three sets: - set1 is created from the list [1, 2, 3, 4] - set2 is created from the list [3, 4, 5, 6] - set3 is created as the difference between set2 and set1.

Calculate the difference between set2 and set1

We are asked to find "set2.difference(set1)", which refers to the set of elements that are in set2 but not in set1. This is also known as the relative complement of set1 in set2. To find the difference between set2 and set1, we take each element in set2 and check if it is present in set1. If it's not present, we include it in the result.

Determine the elements of set3

Performing the difference operation between set2 and set1, we get: - 3: present in both set1 and set2, not included - 4: present in both set1 and set2, not included - 5: present in set2 but not in set1, included - 6: present in set2 but not in set1, included Thus, set3 will have the elements 5 and 6. In mathematical notation, set3 = \\{5, 6\\}.

Key concepts

Python programming

Python is an immensely popular and high-level programming language known for its clear syntax and readability, making it an excellent choice for beginners. It supports multiple programming paradigms, including procedural, object-oriented, and functional programming. Python's standard library is broad, offering modules and functions for variable types, including sets, which play a crucial role in many data manipulation tasks.

When dealing with Python sets, one key aspect to understand is that they are collections of unordered, unique elements. This characteristic is what drives their use in operations that involve handling distinct items, such as union, intersection, difference, and symmetric difference. These operations can be easily performed using Python's built-in methods, which will be explored further in the context of set operations.

Set operations

In the realm of mathematics, a set is a collection of distinct objects, and set operations are the fundamental actions you can perform on these collections. Python implements these operations through built-in methods. One such operation is the difference, which can find the relative complement of two sets.

In Python, the difference between two sets can be computed using the .difference() method. For example, setA.difference(setB) results in a new set that contains all the elements of setA that are not in setB. This method is non-destructive, meaning it does not modify the original sets. It's prudent to remember that the difference operation is not commutative; setA.difference(setB) does not yield the same result as setB.difference(setA), which is a common point of confusion.

Relative complement

The relative complement, also known as the set difference, is a core concept in set theory. It refers to the elements that are in one set but not in another. Symbolically, the relative complement of set B in set A is denoted as A − B. This results in a set of elements that are unique to set A when both sets are compared.

Applied to our Python example from the exercise, set2.difference(set1) resembles the mathematical expression set2 − set1, which means we are extracting elements that exist exclusively in set2. Understanding the direction of the difference is crucial; it determines which set's perspective we use to define 'unique'. This understanding is essential when interpreting results and troubleshooting code that involves set differences.

Python data structures

Data structures are a way of organizing and storing data so that they can be accessed and worked with efficiently. Python includes several built-in data structures, each with its unique properties and use cases. Among these are lists, tuples, dictionaries, and sets.

Sets, as seen in the exercise we've been discussing, are particularly useful when the uniqueness of the elements is necessary. They provide a high-performance way to store non-duplicated items and are optimized for operations like checking for membership, removing duplicates from a sequence, and performing the aforementioned set operations. Using sets in Python can significantly streamline certain tasks that involve collection manipulation, and they are an indispensable tool for many developers and data analysts.