LAWS IN BOOLEAN ALGEBRA
Commutative Law
a.
A+B=B+A
A
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B
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A+B
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B+A
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0
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0
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0
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0
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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b.
A∙B=B∙A
A
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B
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A.B
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B.A
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0
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0
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0
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0
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0
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1
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0
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0 |
1
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0
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0
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0 |
1
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1
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1
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1
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Distributed Law
a. A∙(B+C)=(A∙B)+(A∙C)
A
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B
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C
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B+C
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A∙(B+C)
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A∙B
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A∙C
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(A∙B)+(A∙C)
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0
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0
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0
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0
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0
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0
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0
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0
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0
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0
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1
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1
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0
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0
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0
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0
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0
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1
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0
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1
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0
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0
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0
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0
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0
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1
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1
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1
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0
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0
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0
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0
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1
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0
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0
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0
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0
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0
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0
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0
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1
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0
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1
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1
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1
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0
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1
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1
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1
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1
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0
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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b. A+(B∙C)=(A+B)∙(A+C)
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A
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B
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C
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B∙C
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A+(B∙C)
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A+B
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A+C
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(A+B)∙(A+C)
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0
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0
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0
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0
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0
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0
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0
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1
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0
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0
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0
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1
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0
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0
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1
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0
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0
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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0
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0
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1
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1
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1
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1
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1
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0
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1
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0
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1
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1
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1
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1
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1
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1
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0
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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Associative Law
a. A+(B+C)=(A+B)+C
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A
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B
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C
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B+C
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A+(B+C)
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A+B
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(A+B)+C
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0
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0
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0
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0
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0
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0
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0
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0
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0
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1
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1
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1
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0
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0
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1
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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0
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0
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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b. A∙(B∙C)=(A∙B)∙C
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A
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B
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C
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B∙C
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A∙(B∙C)
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A∙B
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(A∙B)∙C
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0
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0
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0
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0
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1
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1
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. DEMORGAN'S THEOREM:
In demorgan’s theorem there are two types. They are:-
1. (A ∙ B)' = A' + B'
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A
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B
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A∙B
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)' A`
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B`
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A`+B`
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0
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0
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0
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1
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1
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1
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1
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0
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1
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0
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1
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1
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0
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1
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0
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1
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1
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1
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0
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0
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2. (A+B)' = A' ∙ B'
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A
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B
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A+B
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A`
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B`
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A`∙B`
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0
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0
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0
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1
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1
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1
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1
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0
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1
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1
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0
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1
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1
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NEXT TOPIC: BOOLEAN FUNCTIONS