Question

After the following code executes, what elements will be members of set3? set1 = set(['a', 'b', 'c']) set2 = set(['b', 'c', 'd']) set3 = set1.symmetric_difference(set2)

Short answer

Answer: The elements of set3 will be {'a', 'd'}.

Step-by-step solution

Identify the unique elements in each set

To find the symmetric difference of set1 and set2, we need to identify the elements that are unique to each set. In set1, the unique element is 'a', and in set2, the unique element is 'd'.

Combine the unique elements

Combine the unique elements from set1 ('a') and set2 ('d') to create the resulting set containing the symmetric difference of set1 and set2.

Determining the elements of set3

After the given code has been executed, set3 will contain the elements that are unique to set1 and set2. Therefore, set3 will have the elements {'a', 'd'}.

Key concepts

Python Sets

A set in Python is a collection of elements that are both unordered and unindexed. Sets are written with curly braces and are mutable, meaning we can add or remove items after the set has been created. A key feature of a set is that it cannot have duplicate elements; it automatically filters out any duplicates.

When you assign set1 = set(['a', 'b', 'c']) and set2 = set(['b', 'c', 'd']), you're creating two sets with some common elements. In Python sets, you can perform typical mathematical set operations like union, intersection, and difference. The uniqueness of elements in a set makes it particularly useful for these kinds of operations.

Set Operations

Set operations are central to the concept of sets in mathematics. In Python, these operations have been implemented in an intuitive and handy way. For instance, with set3 = set1.symmetric_difference(set2), we use the symmetric_difference method to obtain unique elements, resulting in a new set that contains all items from both sets, except those that are present in both.

Symmetric Difference Explained

The symmetric difference is similar to the XOR operation in logic. It focuses on items that are in either of the sets but not in both simultaneously. To visualize this, picture two overlapping circles in a Venn diagram; the symmetric difference lies in the non-overlapping parts of the circles. This operation is useful in data analysis when one needs to find items that are exclusive to each dataset.

Unique Elements in Sets

The concept of uniqueness is fundamental to sets. When discussing unique elements in the context of set operations, we're referring to the items that do not have duplicates within the set or across multiple sets being analyzed.

In the exercise, identifying the unique elements from set1 and set2 is crucial to finding the symmetric difference. Set1 has 'a' unique to it, while set2 has 'd'. With set operations in Python, such as set1.symmetric_difference(set2), we can find the unique elements across the two sets without manually comparing each item. This showcases the power and efficiency of using set operations in data-related tasks where such comparisons are common.