Laws of Expansion (MA186E)

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
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

 

 

 

 


Circuit Bench