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

question 36

Short Answer

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. $$x = x + 0 = x + ( x \bar { x } ) = ( x + x ) ( x + \bar { x } ) = ( x + x ) \cdot 1 = 1 \cdot ( x + x ) = x + x$$

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Definitions:

Subjective Accounts

Personal perspectives or descriptions of experiences, which are influenced by one's own feelings and opinions.

Physiological Viewpoint

The physiological viewpoint focuses on the biological basis of behavior, emotions, and mental states, emphasizing the role of the brain, nervous system, and other bodily functions.

Conscious Processes

Mental activities of which an individual is fully aware, including thoughts, feelings, and decisions.

Factor Analysis

A statistical approach designed to uncover hidden variables or factors that account for the observed correlation patterns within a set of variables.