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.
10. Cancellation law: For all x, y, and z in B, if and then .
For all in , if .
Let be the Boolean algebra, with the operations, addition” ”and multiplication” ”
Let be the Boolean algebra with operation addition and multiplication .
Suppose are any element of .
Consider the statement.
As be the Boolean algebra and for all and .
By using the above fact that can be written as.
By the commutative law for addition .
By the commutative law for multiplication
By hypothesis .
By the Distributive law for multiplication , over addition
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