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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.

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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