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Give a Reason for Each Step in the Proof That x=x+0=x+(xxˉ)=(x+x)(x+xˉ)=(x+x)1=1(x+x)=x+xx = x + 0 = x + ( x \bar { x } ) = ( x + x ) ( x + \bar { x } ) = ( x + x ) \cdot 1 = 1 \cdot ( x + x ) = x + x

question 14

Essay

Give a reason for each step in the proof that x + x = x is true in Boolean algebras. Your reasons should come from the following: associative laws for addition and multiplication, commutative laws for addition and multiplication, distributive law for multiplication over addition and distributive law for addition over multiplication, identity laws, unit property, and zero property. x=x+0=x+(xxˉ)=(x+x)(x+xˉ)=(x+x)1=1(x+x)=x+xx = x + 0 = x + ( x \bar { x } ) = ( x + x ) ( x + \bar { x } ) = ( x + x ) \cdot 1 = 1 \cdot ( x + x ) = x + x

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Definitions:

Hypothesis

A proposed explanation for a phenomenon, made as a starting point for further investigation, which can be tested through experiments or observations.

Educated Guess

A hypothesis or assumption made based on prior knowledge and rational inferences.

Hypothesis

A proposed explanation for a phenomenon, made as a starting point for further investigation.

Within-Subjects

A research design where the same participants are subjected to all conditions or treatments, allowing for direct comparison of different interventions on the same individual.

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