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About Mr. Minner
 IF you are visiting this page,
THEN you are on the internet!
Surely, all of Mr. Minner's geometry students recognize the significance of this statement as it relates to the study of mathematics.
The statement, written in "if-then" form is a conditional statement. It is another way of saying that
"visitors to this page are on the internet." A student's ability to comprehend statements and/or expressions is the initial step taken towards learning the rules of logic;
and subsequently becoming successful at the study of geometry.
Here is an example of
If-Then in Music.
The statement after the word "IF" is called the hypothesis, while the statement that follows the word "THEN" is referenced as the conclusion.
During the first quarter of our yearly studies students have learned to manipulate
the hypothesis and conclusion in order to define 3 other conditional statements.
- The converse of the conditional "if-then" statement above is formed by exchanging the conclusion with the hypothesis.
"If you are on the internet, then you are visiting this page."
That statement is obviously not true, because you could be on the internet visiting "Google", for example.
The ability to give a counterexample just as was stated in the previous paragraph is proof that the converse of the original conditional statement is false.
- The inverse of a conditional statement requires that the negation of the hypothesis implies that the negation of the conclusion is true.
"If you are not visiting this page, then you are not on the internet."
Mr. Minner is confident that all of his geometry students could provide a counterexample demonstrating that the above inverse statement is invalid.
- The contrapositive of the original conditional statement says that the negation of the original conclusion implies that the negation of the original hypothesis is valid.
"If you are not on the internet, then you are not visiting this page."
What do you think? Is the contrapositive true or false? If it is false then you surely should be able to present a counterexample.
 Much of the study of these logical "head games" can be traced to author, mathematician, clergyman, and photographer Lewis Carroll. Carroll, pictured above, is known for writing
"Alice's Adventures in Wonderland." He has inspired countless people through the generations with his references to logic, syllogism, and games. One of the great rock groups of the 1960's and 1970's, Jefferson Airplane, even wrote a hit song inspired by Carroll called White Rabbit.
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Laurel Intermediate Middle School