Combinational Logic Gates
where:
A = input
B = input
Q = result
AND
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OR
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NOT
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NAND
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NOR
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XOR
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XNOR
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Single Variable Theorems
Identities: A×1=A , A+0=A
Null elements: A×0=0 , A+1=1
Idempotence: A×A=A , A+A=A
Complements: A׬A=0 , A+¬A=1
Involution: (¬A)=A
Where : ¬ = negation or logical NOT
Multivariable Theorems
Commutative: A×B=B×A , A+B=B+A
Associative: (A×B)×C=A×(B×C) , (A+B)+C=A+(B+C)
Distributive: (A+B)×(A+C)=A+B×C , A×B+A×C=A×(B+C)
Covering: A×(A+B)=A , A+A×B=A
Combining: (A+B)×(A+B)=A , A×B+A׬B=A
Consensus: A×B+¬A×C+B×C=A×B+¬A×C ,
(A+B)×(¬A+C)×(B+C)=(A+B)×(¬A+C)
Where: ¬ = negation or logical NOT