CK12 - Geometry

Example 3

Supposethe followingtwo statementsare true.

1.If you love me let me know, if you don’tthen let me go.(A countrymusicclassic.Lyrics by JohnRostill.)

2.You don’tlove me.

Whatis the logicalconclusion?

Let me go.

Thereare two statementsin the first line. The secondone is:

If you don’t(loveme) then let me go.

You don’tlove me is statedto be true in the secondline.

Basedon thesetrue statements,Let me go is the logicalconclusion.

Now let’s look at the structureof all of theseexamples,usingthe and symbolsthat we usedearlier.

Eachof the exampleshas the sameform.

conclusion:

A morecompactform of this argument,(logicalpattern)is:

To statethis differently, we couldsay that the true statement followsautomaticallyfrom the true statements

and.

This reasoningpatternis one of the basicrulesof logic.It’s calledthelaw of detachment.

Law of DetachmentSuppose and are statements.Thengiven

and You can conclude

Practicesayingthe law of detachmentlike this: “If is true, and is true,then is true.”

Example 4