Simplify the following sentences. Try to get simplification that are assimple, or as short as possible. Indicate briefly how the simplification is achieved.
1. A∧B ∨ ¬A∧B
3. (A ∨ B) ∧ (A ∨ ¬B)
5. (A ∨ B∧C) ∧ ¬(B ∧ C)
7. ¬B ∨ B∧A
9. (A ∨ ¬B) ∧ ¬(¬B ∨ A)
11. (¬B ∨ A∧B) ∧ (A ∨ ¬A∧B)
13. (A ∨ B) ∧ (A ∨ ¬B) ∧ (¬A ∨ B) ∧ (¬A ∨ ¬B)