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

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Definitions:

Extraversion

A personality trait characterized by high levels of energy, sociability, talkativeness, and a tendency towards seeking stimulation in the company of others.

Neuroticism

A personality trait associated with negative emotions such as anxiety, depression, and irritation, reflecting how prone an individual is to psychological stress.

Cultural Characteristic

Traits or qualities that define the social practices, norms, arts, beliefs, and other human endeavors considered characteristic of a specific group or society.

Toughness

The quality of being strong and durable, also referring to the ability to endure hardship or stress without compromising one's character.