Laws of Expansion (MA186E)

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Published: Saturday, 04 June 2016 00:00

Written by Newton C. Braga

The disjunction of a product composed of the element a and b and a product composed by element a and the complement of the element b is equivalent to the element a. The conjunction of a sum of the element a and b and a sum composed of the element a and the complement of the element b is equivalent to the element a. Figure 1 shows the circuit diagram describing these laws,

Figure 1

Laws of Expansion:

 

 

Mathematic Notation:

(a ∩ b) ∪ (a ∩ b’) = a

(a ∪ b) ∩ (a ∪ b’) = a

Logic Notation:

(a ∧ b) ∨ (a ∧ ~b) = a

(a ∨ b) ∧ (a ∨ ~b) = a