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:

Product Elasticity

Product elasticity refers to the degree to which the demand for a product changes in response to a change in price.

Income Effect

The change in an individual's or economy's income and how that change will impact the quantity demanded of a good or service.

Complementary Effect

The impact that the improvement or performance of one product or service has on the demand for another that is used in conjunction with it.

Fast-Food Restaurants

Eateries that serve food quickly and efficiently to customers, often characterized by a limited menu of pre-prepared or rapidly cooked items.