Find the minimal value of integer $ n$ that guarantees: 
Among $ n$ sets, there exits at least three sets such that any of them does not include any other; or there exits at least three sets such that any two of them includes the other. 

$\textbf{(A)}\ 4  \qquad\textbf{(B)}\ 5  \qquad\textbf{(C)}\ 6  \qquad\textbf{(D)}\ 7  \qquad\textbf{(E)}\ 8$
To solve this problem, we need to find the minimal value of \( n \) such that among \( n \) sets, there exist at least three sets such that any of them does not include any other, or there exist at least three sets such that any two of them include the other.

1. **Understanding the Problem:**
   - We need to ensure that among \( n \) sets, there are either:
     - Three sets where none of them is a subset of another, or
     - Three sets where each pair of sets has one set that is a subset of the other.

2. **Analyzing the Subset Relationships:**
   - Consider the possible relationships between sets:
     - If \( A \subset B \), then \( A \) is a subset of \( B \).
     - If \( A \cap B = \emptyset \), then \( A \) and \( B \) are disjoint sets.

3. **Constructing Examples:**
   - Let's start with a smaller number of sets and increase until we find the minimal \( n \) that satisfies the condition.
   - For \( n = 3 \):
     - We can have sets \( A, B, C \) such that \( A \subset B \subset C \). This does not satisfy the condition because there are no three sets where none is a subset of another.
   - For \( n = 4 \):
     - We can have sets \( A, B, C, D \) such that \( A \subset B \subset C \subset D \). This still does not satisfy the condition.
   - For \( n = 5 \):
     - Consider sets \( A, B, C, D, E \) with the following relationships:
       - \( A \subset B \subset C \)
       - \( D \) and \( E \) are disjoint from \( A, B, C \) and from each other.
     - In this case, \( A, D, E \) are three sets such that none of them is a subset of another.

4. **Verification:**
   - We need to verify that \( n = 5 \) is indeed the minimal number.
   - For \( n = 4 \), we cannot find three sets where none is a subset of another or where each pair of sets has one set that is a subset of the other.
   - Therefore, \( n = 5 \) is the minimal number that satisfies the condition.

The final answer is \( \boxed{5} \)