CK12 - Geometry

2. If Markis late, Wen will be late.


3. If Wen is late, Karl will be late.

To these,add one moretrue statement.

4. Pete is late.

One clearconsequenceis: Markwill be late. But makesure you can see that Wen and Karl will also be
late.

Here’s a symbolicform of the statements.

1.

2.

3.

4.

Our statementsform a “chainreaction.”Each“then”becomesthe next “if” in a chainof statements.The

chaincan consistof any numberof connectedstatements.Oncewe add the true statementas above,
we knowthat the conclusion(the then part) of the last statementis justified.

Anotherway to look at this is to imaginea chainof dominoes.The dominoesare the linkedif-thenstatements.

Oncethe first dominofalls, eachdominoknocksthe next one over, and the last dominofalls. is the tipping
over of the first domino.The final conclusionof the last if-thenstatementis the last domino.

This is calledthe law of syllogism. A formalstatementof this rule of logic is givenbelow.

Law of SyllogismSuppose , , ..., , and are statements.Thengiventhat

is true and that you havethe followingrelationship:

Then,you can conclude

Inductivevs. DeductiveReasoning

You havenow workedwith bothinductiveanddeductivereasoning.Theyare differentbut not opposites.In
fact, they will worktogetheras we studygeometryand othermathematics.

How do thesetwo kindsof reasoningcomplement(strengthen)eachother?Thinkaboutthe examplesyou
saw earlierin this chapter.