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 $a \mid c$ .

Understand the basic properties of vectors in Java, such as size, capacity, and memory management methods.

Learn the distinction between collection size and capacity, and the process of handling primitive types in collections.

Grasp the significance of Java's util package for the Collection Framework and recognize methods not part of the Collection interface.

Appreciate the limitations and capacities related to specific implementations like HashMap.

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Definitions:

Mere Exposure Effect

A psychological phenomenon by which individuals develop a preference for people or things simply because they are familiar with them.

Altruism

The selfless concern for the well-being of others.

Blaming the Victim

The unjust practice of holding the victim of a crime or misfortune responsible for their own hardship.

Just-World Phenomenon

The belief that people get what they deserve, leading to a sense that the world is fair and just.