1. **State the problem:** Simplify the boolean expression $$(A + \overline{B})(C + \overline{B})(B + (\overline{B} + \overline{C})) + A + B + C$$ and determine which option it matches. 2. **Simplify inside the third parenthesis:** $$B + (\overline{B} + \overline{C}) = B + \overline{B} + \overline{C}$$ Since $B + \overline{B} = 1$ (covering all possibilities), we have $$1 + \overline{C} = 1$$ So $$B + (\overline{B} + \overline{C}) = 1$$ 3. **Substitute back:** The expression becomes $$(A + \overline{B})(C + \overline{B})(1) + A + B + C = (A + \overline{B})(C + \overline{B}) + A + B + C$$ 4. **Multiply the two terms:** $$(A + \overline{B})(C + \overline{B}) = AC + A\overline{B} + C\overline{B} + \overline{B}\overline{B}$$ Remembering $\overline{B}\overline{B} = \overline{B}$, we get $$AC + A\overline{B} + C\overline{B} + \overline{B} = AC + A\overline{B} + C\overline{B} + \overline{B}$$ Since $\overline{B}$ covers $A\overline{B}$ and $C\overline{B}$ (by absorption), this reduces to $$AC + \overline{B}$$ 5. **Rewrite the expression:** $$AC + \overline{B} + A + B + C$$ Note that $$\overline{B} + B = 1$$ So the expression becomes $$AC + 1 + A + C$$ 6. **Any boolean OR with 1 is 1:** $$AC + 1 + A + C = 1$$ 7. **Final answer:** The given boolean expression simplifies to **1**. Therefore, the correct choice is $\boxed{1}$.