Here Is a Sample Proof That Contains an Error $a \mid b$

question 109

Essay

Here is a sample proof that contains an error. Explain why the proof is not correct.
Theorem: If $a \mid b$ and $b \mid c$ , then $a \mid c$ .
Proof: Since $a \mid b , b = a k$ .
Since $b \mid c , c = b k$ .
Therefore $c = b k = ( a k ) k = a k ^ { 2 }$ .
Therefore $a \mid c$ .

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Definitions:

Binding Price Ceiling

A legally imposed price limit that is set below the equilibrium price, leading to a shortage as demand exceeds supply at that price level.

Graph (a)

A graph is a visual representation of relationships between two or more variables or sets of data, often using lines, bars, or points in a two-dimensional or three-dimensional space.

Price Control

Government-imposed limits on the price charged for commodities and services in an effort to curb inflation or ensure affordability.

Public's Need

Refers to the essential goods, services, and conditions necessary for the well-being of a community or population.