`(AuuB)-C=(A-C)uu….`

Answer

To solve the equation \((A \cup B) - C = (A - C) \cup \text{?}\), we will use the concept of Venn diagrams to visualize the sets involved and find the missing set in the right-hand side (RHS) of the equation.

### Step-by-Step Solution:

1. **Understanding the Left-Hand Side (LHS)**:
- The LHS is \((A \cup B) - C\).
- This means we take the union of sets A and B, and then remove the elements that are in set C.
- In a Venn diagram, we will shade the entire area of A and B, but we will not shade the area that overlaps with C.

2. **Drawing the Venn Diagram for LHS**:
- Draw two overlapping circles representing sets A and B.
- Shade the entire area of both circles (A and B) but leave out the area that overlaps with circle C.
- The shaded area represents \((A \cup B) - C\).

3. **Understanding the Right-Hand Side (RHS)**:
- The RHS is \((A - C) \cup \text{?}\).
- Here, \(A - C\) means we take set A and remove any elements that are also in set C.
- In the Venn diagram, we will shade the part of A that does not overlap with C.

4. **Drawing the Venn Diagram for \(A - C\)**:
- In the same Venn diagram, shade the part of circle A that does not overlap with circle C.
- This shaded area represents \(A - C\).

5. **Finding the Missing Set**:
- Now, we need to find what should be shaded along with \(A - C\) in order to make the RHS equal to the LHS.
- From our LHS shading, we see that the remaining shaded area corresponds to the part of set B that does not overlap with C.
- Therefore, the missing set can be represented as \(B - C\).

6. **Final Equation**:
- We can now write the complete RHS as:
\[ (A - C) \cup (B - C) \]
- Thus, we have:
\[ (A \cup B) - C = (A - C) \cup (B - C) \]

### Conclusion:
The complete equation is:
\[ (A \cup B) - C = (A - C) \cup (B - C) \]