Question

How can you determine whether a specific element exists in a set?

Short answer

Question: Explain the step-by-step process to perform a membership test on a given set for a specific element. Answer: The step-by-step process to perform a membership test on a given set for a specific element involves the following steps: 1. Identify the given set and the element to be tested for membership. 2. Use a membership test, such as "in" keyword in Python or "contains" method in Java. 3. Apply the membership test to the given set and element using the chosen programming language. 4. Interpret the result - if the result is true, the element exists in the set; if the result is false, the element does not exist in the set.

Step-by-step solution

Understand the given set and elements

First, identify the given set and the elements that need to be tested for membership. Suppose you are given a set S and an element x. We want to determine if x exists within S.

Using membership test

To perform a membership test, we check if x is present as a member of the set S. This can be done using the “in” keyword in Python, or by using the set's method "contains" in Java, for example. In mathematical notation, we represent this process by writing the element followed by the symbol "∈" and then the set: x ∈ S

Performing the membership test

Apply the membership test to the given set S and the element x. In Python, you can use the following code: ```python x in S ``` In Java, you can use the following code: ```java S.contains(x) ``` For example, if the given set is S = {1, 2, 3, 4, 5} and you want to check if the element 3 exists in the set: In mathematical notation: 3 ∈ S In Python: ```python S = {1, 2, 3, 4, 5} x = 3 result = x in S ``` In Java: ```java Set S = new HashSet<>(Arrays.asList(1, 2, 3, 4, 5)); int x = 3; boolean result = S.contains(x); ```

Interpret the result

After the membership test, if the result is true, the element exists in the set; if the result is false, the element does not exist in the set. In our example, since 3 is a member of the set {1, 2, 3, 4, 5}, the result will be true.