We are tasked with finding how many elements are in $B$ but not in $A$. Let's break the problem down step by step.

Information provided:

1. Universal set $S$ has $69$ elements.
2. $|A| = 16$ (Set $A$ contains 16 elements).
3. $|B| = 26$ (Set $B$ contains 26 elements).
4. $|A \cap B| = 1$ (Set $A$ and $B$ have 1 element in common).

We need to find $|B - A|$, the number of elements in $B$ but not in $A$.

Calculation:

1. The elements in $B$ but not in $A$ are given by: $|B - A| = |B| - |A \cap B|$

2. Substitute the values: $|B - A| = 26 - 1$

3. Simplify: $|B - A| = 25$

Final Answer:

The number of elements in $B$ but not in $A$ is: $\boxed{25}$

Would you like me to expand on this or explore related concepts?

Related Questions:

1. How do we calculate $|A \cup B|$ using this data?
2. What is the total number of elements outside both $A$ and $B$?
3. How can the principle of inclusion-exclusion be applied here?
4. How many elements are in $A$ but not in $B$?
5. How do we confirm that the universal set $S$ is consistent with these values?

Tip:

Always visualize sets and their relationships with Venn diagrams to clarify overlapping and non-overlapping regions.