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# Math and Advertising? How?

In the business world, the typical components of an advertisement are:

• The Product and Its Features
• The Price of The Product
• Promises of What the Product Will Do

The promises may or may not be backed up by what we call a "guarantee".  The promises and guarantee must have the following features:

• The guarantee, if it is made, must not run the company into bankruptcy.  i.e. It must not be too good.
• The promises must be kept so as not be classified as false advertising.

So how do you make up a guarantee that does not bankrupt your company yet is completely legal? Also, how can you avoid being guilty of false advertising?

Answer: You rely on logic. Math, at its heart, is based on deductive logic.  We prove that If certain conditions are met, then a certain conclusion may be made.  We make conclusions using deductive logic. In mathematics, we also disprove if-then type statements. In other words, we prove that an if-then statement is false.

In the business world, a false if-then statement amounts to a false promise.  This is the equivalent of fraud!

How does a business avoid being guilty of fraud?

Answer: Use of quantifiers.

Here is an example of two statements.  One has additional clauses and one does not.

 WITHOUT ADDITIONAL CLAUSES WITH ADDITIONAL CLAUSES If x = 3, then x + 2 = 6This is a false statement.  If you put this on your math test, you would get points deducted. If x = 3 and x +2 = 4, then x+2 = 6This is a true statement.  Why? The if-part is not true.  And when the if-part is not true, then entire if-then statement remains true.  Pretty tricky eh?

Here is a similar set of examples, applied to the actual guarantee of a weight loss product Fatburn.com.

 WITHOUT ADDITIONAL CLAUSES WITH ADDITIONAL CLAUSES If youUse our weight loss product and do not experience the weight loss you hoped for, and you request a refund. Then you will be refunded your money. Let's say a person uses the product but loses only 5 pounds instead of the 15 pounds hoped for.  This person requests a refund but is denied. This is then a false statement made by the advertiser. The advertiser would be subject to fines and shutdown from the FTC. There really are no specific conditions to be met so the manufacturer is legally obligated to refund the purchase price on nearly any request, leading to large profit losses. If you meet the conditions Use the weight loss site each day to accurately enter your foods, weight, and activities. Show a weekly deficit of 3,500 calories. Take in a minimum of 1,000 calories each day if you are a woman and 1,500 calories each day if you are a man. (Taking in less than these minimums can be unhealthy.) yet you do do not experience the weight loss you hoped for, and you request a refund. Then, you will be refunded your money. Let's suppose you are not pleased with this product but  you forget to use the weight loss site one day AND you request a refund, but your refund is denied.  Has the company made a false promise? This company has not made a false statement.  Why? Again, the if-part is not true. The customer did not satisfy all the conditions.

Of course the company cited in this example, Fatburn.com, may choose to overlook all of the conditions and in fact grant a refund even if not quite all of the conditions are met.  But, they are not legally obligated to do so.

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