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Commutation

The commutative law states that the inter-changing of the order of operands in a Boolean equation does not change its result.

  • Using the OR operator → A + B = B + A
  • Using the AND operator → A * B = B * A

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Quick Reference

Commutative Law

(a) A + B = B + A
(b) A B = B A

 Associate Law

(a) (A + B) + C = A + (B + C)
(b) (A B) C = A (B C)

 Distributive Law

(a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A + C)

 Identity Law

(a) A + A = A
(b) A A = A

(a) 
(b) 

 Redundance Law

(a) A + A B = A
(b) A (A + B) = A

(a) 0 + A = A
(b) 0 A = 0

(a) 1 + A = 1
(b) 1 A = A

(a) 
(b) 

(a) 
(b) 

 De Morgan's Theorem

(a) 
(b) 

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