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boolean laws, - - Coggle Diagram
boolean laws
Associate Law
A.(B.C) = (A.B).C = A.B.C (AND Associate Law)
e.g. 5+ (6+2) = 13, 6 + (5+2) = 13
A + (B+C) = (A+B) + C = A+B+C (OR Associate Law)
This law allows the removal of brackets from an expression and regrouping of the variables.
Complement Law
A variable AND its complement equals 0
A.Ā = 0
A variable OR its complement equals 1
A + Ā = 1
Distributive Law
This law is similar to distributivity in normal mathematics and has to do with expanding or simplifying brackets. This may be done when an AND or OR is inside the brackets and another is outside.
You will use this often
A + (B.C) = (A + B).(A + C)
Identity law
The identity law observes how certain expressions behave when one of the terms is fixed.
:dolphin:
A variable OR 0 is always equal to the variable
A+0 = A
A variable AND 1 is always equal to the variable
A.1 = A
Commutative Law
Commutative law states that the order of terms in an expression (or part of an expression within brackets) may be reordered and the result will not be affected. This applies to both OR and AND
Annulment Law
A.0 = 0 - A variable AND 0 equals 0
A + 1 = 1 - A variable OR 1 equals 1
Double Complement Law
This law states that if you negate a negation (i.e. if you have a NOT within a NOT) they cancel each other out.
(Ā) = A
Idempotent Law
This law handles repeated variables within an expression by simplifying it to itself.
A variable OR itself is always equal to the variable
A+A = A
A variable AND itself is always equal to the variable
A.A = A
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