What Is the Law of Syllogism in Geometry?

What Is the Law of Syllogism in Geometry?

What Is the Law of Syllogism in Geometry?

The law of syllogism in geometry states that "if p, then q," and "if q then r." It’s also possible to derive a third statement that "if p, then r." The “if-then” statement applies to the law of syllogism to aid in deductive reasoning.

For example, if Jane encounters a traffic jam today, she reports to work late, and if Jane reports to work late, her boss penalizes her. Letting "p" be the statement “encounters a traffic jam today,” "q" be the statement “reports to work late” and "r" be the statement “her boss penalizes her,” by the law of syllogism, a third statement may be deduced that if Jane encounters a traffic jam today, her boss will penalize her.

The relationship between "p" and "q," which is p ? q and read as "if p, then q," is called a conditional statement and involves a hypothesis that’s followed by a conclusion. For example, if 50 percent of students in a class is male, then 50 percent of the class must be female. Interchanging positions of the hypothesis and its conclusion result in the converse statement: if 50 percent of students in a class is female, then 50 percent of the class must be male. A conditional statement and its converse don’t have the same implications.