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The complement law is a fundamental principle in Boolean algebra that states that the conjunction (AND operation) of a variable and its complement equals zero, while the disjunction (OR operation) of a variable and its complement equals one. Mathematically, this can be expressed as ( A \cdot \overline{A} = 0 ) and ( A + \overline{A} = 1 ), where ( A ) is a Boolean variable and ( \overline{A} ) is its complement. This law is essential for simplifying Boolean expressions and designing digital circuits.

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