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:
a.
b.
(a)
To Prove:
Given information:
Let
Concept used:
And
Calculation:
Let
The identity element with respect to addition is
The uniqueness or the complement law tells that, for all
(b)
To Prove: