1. **State the problem:** We have Set A with 10 elements, the total number of elements in either Set A or Set B (the union) is 35, and the intersection of Sets A and B has 6 elements. We need to find the number of elements in Set B. 2. **Formula used:** The formula for the union of two sets is: $$|A \cup B| = |A| + |B| - |A \cap B|$$ where $|A|$ is the number of elements in Set A, $|B|$ is the number of elements in Set B, and $|A \cap B|$ is the number of elements common to both sets. 3. **Substitute the known values:** $$35 = 10 + |B| - 6$$ 4. **Simplify the equation:** $$35 = 10 - 6 + |B|$$ $$35 = 4 + |B|$$ 5. **Solve for $|B|$:** $$|B| = 35 - 4$$ $$|B| = 31$$ **Final answer:** The number of elements in Set B is $31$.