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Boolean Algebra - What laws apply?

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> How can the top statement be equal to the bottom?

It isn't. Consider ¬A ∧ C:

A ∧ (¬B ∨ C) = ⊥ ∧ (¬B ∨ ⊤) = ⊥ ∧ ⊤ = ⊥

C ∨ (¬B ∧ A) = ⊤ ∨ (¬B ∧ ⊥) = ⊤ ∨ ⊥ = ⊤

Also: truth table:

    A B C | A∧(¬B∨C) C∨(¬B∧A)
    ------+------------------
    F F F | F         F
    F F T | F         T *
    F T F | F         F
    F T T | F         T *
    T F F | T         T
    T F T | T         T
    T T F | F         F
    T T T | T         T

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