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.
7. Uniqueness of 1: There is only one element of B that is an identity for •.
There is only one element of that is an identity for.
Let be the Boolean algebra, with the operations, addition” ”and multiplication” ”
Let be the Boolean algebra, with the operations, addition and multiplication .
Suppose are tile identity elements of with respect to multiplication .
To show that there is only identity element of with respect to multiplication it is enough to show that .
The Identity law for multiplication tells that, for all .
It follows that,
Add both sides with ,
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