Basic laws and formulas in logical algebra

1. axiom of logic algebra: (1) If a is not equal to zero, then a =1; If a is not equal to 1

A=0。 (2)0+0=0; 1+ 1= 1; 0+ 1= 1; 1+0= 1;

(3)0*0=0; 1* 1= 1; 1*0=0; 0* 1=0;

(4)0 = 1 NOT gate; 1 = 0 NOT gate;

2. Logical algebra theorem;

( 1)A+0 = A； a+ 1 = 1； A+A = A； (2)A and 0 = 0; A and1= a; A and a = a

(3)A+A NOT gate =1; One and one NOT gate = 0; (A = A NOT gate.

3. Laws of logical algebra:

(1) switching rule: A AND gate B=B AND gate A; A+B = b+ A；

(2) Distribution law: A and gate (B+C)=A and gate B+A and gate C;

A+B AND gate C=(A+B) AND gate (A+C)

(3) the law of association: a and gate (b and gate C)=(A and gate b) and gate c; A+(B+C)=(A+B)+C

(4) absorption law: A+A and AND gate c = a.

(5) De Morgan's Law: (A+B) not =(A NOT gate) and (B NOT gate)