Page 32 - CITS - Electronic Mechanic - TT - 2024

ELECTRONICS MECHANIC - CITS

Complementation Law /Negation Law:

Law1: A·A’=0
Proof:
Case1: If A=0όA’= 1 So, A·A’=0·1=0
Case2: If A =1όA’= 0 So, A·A’=1·0=0
Double Negation Law:
This law states that double negation of a variables is equal to the variable itself.
Law1: A’’=A
Proof:
Case1: If A= 0όA’’= 0’’= 1’= A
Case 2: If A = 1όA’’ =1’’=0’=A
Any odd no.of inversion is equivalent to single inversion.
Any even no.of inversion is equivalent to no inversion at all.
Identity Law:

Case1 : If A=1όA·1=1·1=1=A
Case2 : If A=0όA·0=0·0=0=A
Law2 : A+ 1 = 1
Proof:
Case 1: If A=1όA+1=1+1=1=A
Case 2: If A=0όA+0=0+0=0=A
Null Law:
Case1: If A=1όA·0=1·0=0=0
Case2: If A=0όA·0=0·0=0=0
Law 2: A+ 0 = A
Proof:
Case 1: IfA=1όA+0=1+0=1=A
Case 2 : IfA=0όA+0=0+0=0=A
Absorption Law:
Law1: A+AB = A
Consensus Theorem:
Theorem1:

A·B +

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CITS : E & H - Electronics Mechanic - Lesson 5 - 8