Digital Logic Boolean Algebraic Properties

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Last updated 1:11 AM on 9/8/26
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10 Terms

1
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Commutative:

A + B = B + A | AB = BA

2
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Associative:

A + (B + C) = (A + B) + C | A(BC) = (AB)C

3
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Identity:

A + 0 = A | 0 + A = A | (A)1 = A | 1(A) = A

4
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Null:

A + 1 = 1 | 1 + A = 1 | (A)0 = 0 | 0(A) = 0

5
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Complement:

A + A’ = 1 | A’ + A = 1 | AA’ = 0 | A’A = 0

6
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Idempotency:

A + A = A | AA = A

7
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Involution:

(A’)’ = A

8
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Distributive:

A(B + C) = AB + AC | A + BC = (A + B)(A + C)

9
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Adjacency:

AB + AB’ = A | (A + B)(A + B’) = A

10
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Simplification:

A + A’B = A + B | A(A’ + B) = AB