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State Boolean laws.Elucidate how they ar...

State Boolean laws.Elucidate how they are used to simplify Boolean expressions with suitable example,

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Laws of Boolean algebra:
Complement law:

The complement law can be realised as `bar(A) =A`

The Boolean operations obey the following laws:
Commutative laws:
`A+B=B+A`
`A.B=B.A`
Associate laws:
`A+(B+C)=(A+B0+C`
`A.(B.C)=(A.B).C`
Distributive laws :
`A(B+C)=AB+BC`
`A+BC=(A+B)(A+C)`
The above laws are used to simplify complicated expressions and to simplify the logic circuitry.
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