It seems you've uploaded an image containing logical algebraic expressions for simplification. Let me extract and process each of the Boolean algebra problems in the image to provide solutions.

Here’s a breakdown of the exercise:

1. $\overline{x} + x y$ (Apply the distributive property for simplification)
2. $x (x + y)$
3. $x y + x z + y z$
4. $\overline{(x y)} + z$
5. $\overline{abc} + abc + abc + \overline{abc}$
6. $ab + ac + bc$
7. $\overline{a}c + ab + abc + bc$
8. $x y z + x y z + x y z + x y z$
9. $\overline{x} y z + x y z + x y z + x y z + x y z$
10. $\overline{x} y z + x y z + x y z + x y z + x y z$
11. $S = A + AB + ABC + ABCD$

Would you like to proceed with a detailed solution for these? Let me know if you'd like me to explain or simplify them step-by-step!