Give a Reason for Each Step in the Proof That

question 59

Essay

Give a reason for each step in the proof that x + xy = 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, zero property, and idempotent laws. $$\begin{array} { l } x + x y = x \cdot 1 + x y = x ( y + \bar { y } ) + x y = ( x y + x \bar { y } ) + x y = x y + ( x y + x \bar { y } ) = ( x y + x y ) + x \bar { y } = x y + x \bar { y } = \\x ( y + \bar { y } ) = x \cdot 1 = x\end{array}$$

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Definitions:

Hypnotized Subjects

Individuals who are in a state of hypnosis, characterized by increased focus, concentration, and openness to suggestion.

Control

The power to influence or direct people's behavior or the course of events.

Hand Rise

A gesture involving lifting one or both hands, often used to signal attention, readiness, or the desire to speak in a group setting.

Physiological Reactions

Refers to the body's automatic responses to stimuli, involving various biological reactions such as changes in heart rate, breathing, or skin temperature.