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.Continue Reading
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.Learn more about Geometry