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

question 51

Short Answer

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:

Save a Life

Save a Life refers to actions or interventions taken to prevent someone from dying.

Marginal Cost Curve

A graphical representation showing how the cost of producing one more unit of a good changes as production volume varies.

Upward Sloping

A line on a graph that shows an increase in a certain variable as another variable increases.

Sunk Costs

Costs that have already been incurred and cannot be recovered, and therefore, should not be considered in making future economic decisions.