13.	+Law+of++Detachment

 Law of Detachment

 The  ** Law of Detachment **  applies when using  **Deductive Reasoning ** **. **  The **Law of Detachment** states that if p-->q is a true conditional statement and p is true, then q is true.  Example: //If it rains, Paul will not go swimming. It is raining.//  You Can conclude that: //Paul will not go swimming.// However, if you were given the same statement: //If it rains, Paul will not go swimming.// And was then told: //Paul did not go swimming// // You // // **cannot **  form a conclusion. Just because Paul went swimming does not mean it rained. In order to form a conclusion you **<span style="font-family: Verdana,Geneva,sans-serif; font-size: 110%; font-style: normal;">must ** <span style="font-family: Verdana,Geneva,sans-serif; font-size: 110%; font-style: normal;"> **<span style="font-family: Verdana,Geneva,sans-serif; font-size: 110%; font-style: normal;">be told that P is true. ** //<span style="font-family: 'Comic Sans MS',cursive; font-size: 80%;"><span style="font-family: 'Comic Sans MS',cursive; font-size: 130%;">//***Reminder p always implies q, but q does not have to imply p**//. <span style="font-family: 'Courier New',Courier,monospace; font-size: 110%; font-style: normal;"> <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; font-style: normal;"> <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 13px; font-style: normal; line-height: 19px;">Example Problems: <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-style: normal; font-weight: normal; line-height: 19px;"> <span style="font-family: 'Arial Black',Gadget,sans-serif;"> A. 1) If two angles are vertical, then their measures are equal. 2) Angle 1 and Angles 2 are vertical.

What can you conclude? You can conclude that the measure of angle 1 and the measure of angle 2 are equal.

B. 1) If you eat breakfast, then you will feel better at school. 2) Kevin ate breakfast.

What can you conclude? You can conclude that Kevin felt better at school.

C. 1)If John is at the bus stop on time, then he will not be late to class. 2) John was late to class.

What can you conclude? You cannot not draw a conclusion. Even though John was late to class, we cannot conclude that he was late to the bus stop. He could have been late for various reasons.

<span style="font-family: 'Courier New',Courier,monospace; font-size: 110%; font-style: normal;">For more practice, visit these sites: <span style="font-family: Verdana,Geneva,sans-serif; font-size: 110%; font-style: normal;"> <span style="font-family: 'Arial Black',Gadget,sans-serif;">[|http://www.ru4math.org/Geometry/If---then---logic-4web.pdf] <span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 110%; font-style: normal;"> <span style="font-family: 'Arial Black',Gadget,sans-serif;"> @http://scienceray.com/mathematics/geometry/geometry-help-deductive-reasoning/ [|www.archmereacademy.com/Portals/101/More%20Laws%20Practice.pdf] <span style="font-family: 'Courier New',Courier,monospace;">