Construct a Complete Truth Table for Each of the Following $\lor$

question 138

Essay

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample.
-X $\lor$ Z
X ⊃ (Y $\lor$ Z)
∼Z ⊃ Y / Y

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Definitions:

Juvenile Detention

A facility where underage individuals are held temporarily as they await court decisions or serve time for their offenses.

Prison Violence

Acts of aggression and conflict occurring within prison facilities, involving inmates, and sometimes staff, posing significant challenges to security and rehabilitation.

Penal System

The network of agencies and processes established by governments to manage individuals accused and convicted of crimes, including law enforcement, courts, and correctional institutions.

Recidivism

The tendency of a convicted criminal to reoffend, often used as a measure of the effectiveness of criminal justice systems.