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Can you explain the rule of distributivity for Boolean algebra?
A + (B C) = (A + B) (A + C)
How does this make sense?
1 Answer
- Anonymous1 decade agoFavorite Answer
Maybe it would help to work the problem
the other direction to see that they really
are equal.
Given:
A + (B C) = (A + B) (A + C)
Work with the right side to produce the left.
(A + B) (A + C)
Distribute the operations (using FOIL):
AA + AC + AB + BC
Reduce AA = A
A + AC + AB + BC
Factor:
A(1 + C + B) + BC
Use 1 + "anything" = 1
A(1) + BC
Reduce:
A + BC
Therefore:
A + (B C) = A + BC
proven.