Examples of Biconditional Statements

September 7, 2011 – Elementary geometry may be the easiest branch of Mathematics since it only deals with definitions and identifications of different shapes and figures like polygons. However, advanced geometry is more challenging since the lessons taught are more complex and hard. In college, geometry lesson plans include ‘logic’ as fundamental topics for higher geometry. This involves complex terms and ideas like the different types of logical reasoning and different types of logical statements which can be used in proving different mathematical theorems and solving different mathematical problems.

One such lesson you might encounter is the discussion of biconditional statements. What are biconditional statements?

Biconditional statements are compound statements formed from two conditions that must be met. So, in order for you to come up with a biconditional statement, you need to be able to satisfy the set conditions first. Take the following statements for an example:
(A) A polygon with less than three sides is not a triangle; and
(B) A polygon with more than three sides is not triangle.

Statements A and B can be written in one compound statement by first making sure that both conditions are met. A more concise way of saying both conditions in one compound statement is to say that “A polygon is a triangle if and only if it has three sides.”, by saying this, we now forma biconditional statement.

This biconditional statement is basically an abbreviated way of saying that (1) if a polygon is a triangle, then it has three sides; and (2) if it has three sides, then the polygon is a triangle. Both statements have the same truth value so they are actually just the converse of the other. When we say truth value, what we mean is that if statement 1 is true, then statement 2 should be true 2, or that if statement 1 is false, then statement 2 should be false too to be considered a good biconditional statement.

 

 

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