b) \( 3-\{2-[3-(4+6)-(2-3)]\}+1 \)

To solve \( 3-\{2-[3-(4+6)-(2-3)]\}+1 \), let's break it down step by step: 1. First, simplify the innermost parentheses: \( 4+6 = 10 \). 2. This makes the equation look like: \( 3-\{2-[3-10-(2-3)]\}+1 \). 3. Next, simplify \( 2-3 = -1 \), leading to: \( 3-\{2-[3-10-(-1)]\}+1 \). 4. Now, simplify inside the brackets: \( 3-10-(-1) = 3 - 10 + 1 = -6 \). 5. This gives us: \( 3-\{2-(-6)\}+1 \). 6. Simplifying further, we find: \( 2-(-6) = 2 + 6 = 8 \), so it becomes \( 3-\{8\}+1 \). 7. Now, calculate \( 3 - 8 + 1 = -5 + 1 = -4 \). Final answer: \( -4 \)