In the image, the question seems to involve set theory. Here's the question, extracted for clarity:

• Let the Universal Set $S$ have 87 elements.
• Set $A$ and $B$ are subsets of $S$.
• Set $A$ contains 43 elements, and Set $B$ contains 35 elements.
• If Sets $A$ and $B$ have 26 elements in common, how many elements are in $A$ but not in $B$?

Solution Approach:

The number of elements in $A$ but not in $B$ is represented by $|A \setminus B|$, which is the difference between the number of elements in $A$ and the number of elements that $A$ shares with $B$ (i.e., the intersection of $A$ and $B$).

Given:

• $|A| = 43$ (the number of elements in set $A$),
• $|B| = 35$ (the number of elements in set $B$),
• $|A \cap B| = 26$ (the number of elements common to both $A$ and $B$).

To find $|A \setminus B|$ (the elements in $A$ but not in $B$): $|A \setminus B| = |A| - |A \cap B|$ Substitute the known values: $|A \setminus B| = 43 - 26 = 17$

Thus, there are 17 elements in set $A$ but not in set $B$.

Would you like more details or further clarification on any step?

Follow-up Questions:

1. How would you calculate the number of elements in $B \setminus A$?
2. Can you find how many elements are in $A \cup B$ (the union of sets $A$ and $B$)?
3. What would be the result if $A$ and $B$ had no elements in common?
4. How can we express $|A \cup B|$ using the inclusion-exclusion principle?
5. How does the universal set $S$ influence this problem, if at all?

Tip:

When dealing with set theory, the inclusion-exclusion principle is very useful for handling problems involving unions and intersections of sets.