In 4—10 assume that B is a Boolean algebra with operations + and•. Prove each statement using only the axioms for a Boolean algebra and statements proved in the text or in lower-numbered exercises.
5. Complements of 0 and 1:
Let be the Boolean algebra, with the operations, addition and multiplication .
Let be the Boolean algebra, with the operations, addition and multiplication
The identity element with respect to addition is and the identity element with respect to multiplication is .
The uniqueness or the complement law tells that, for all , if
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