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# Prove the following absorption properties of Boolean algebras. Give a reason for each step.?

Prove the following absorption properties of Boolean algebras. Give a reason for each step.

x + (x * y) = x and x * (x + y) = x

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- atsuoLv 61 month ago
x + (x * y) = (x * 1) + (x * y) because x = x * 1

(x * 1) + (x * y) = x * (1 + y) by distibution law

x * (1 + y) = x * 1 because 1 + y = 1

x * 1 = x

x * (x + y) = (x + 0) * (x + y) because x = x + 0

(x + 0) * (x + y) = x + (0 * y) by distribution law

x + (0 * y) = x + 0 because 0 * y = 0

x + 0 = x

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