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Babies are illogical. Nobody is despised who can manage a crocodile.

Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons are despised. Lewis Carroll. Rewriting these in an If - then format helps to clarify the preceding statements. If a person is a baby, then the person is not logical.

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Babies are illogical. Nobody is despised who can manage a crocodile.

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  1. Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons are despised. Lewis Carroll Rewriting these in anIf -thenformat helps to clarify the preceding statements. Ifa person is a baby,thenthe person is not logical. If a person is not despised, then that person can manage a crocodile. Ifa person is not logical,thenthe person is despised. What is the logical conclusion of these statements? …\GeoSec02_02.ppt

  2. If-thenstatements are calledconditional statementsor conditionals. Hypothesis- is theIfpart (less theif), and the Conclusion- is thethenpart (less thethen) of the conditional. Ifp,thenq, wherepandqare some statement, is represented symbolically withpq. Symbolically,ifp, thenq(original), becomespq …\GeoSec02_02.ppt

  3. Notice that all statements may not be anif-thenstatement format. Parallel lines don’t intersect. How would you arrange this to make anif-thenstatement? Iflines are parallel, thenthey do not intersect. Linear pairs are supplementary. How would you arrange this to make anif-thenstatement? Iftwo angles are a linear pair,thenthey are supplementary angles. …\GeoSec02_02.ppt

  4. When you are converting sentences toif-thenstatement, look for the key words, if and then. In our examples theif-partis always first, but some sentences may have theif-partat the end of the sentence. For example, I will go to your house, ifit rains tomorrow. Thehypothesisof this sentence is “it rains tomorrow” and theconclusionis “I will go to your house.” To make this a conditional statement it would be rearranged as follows. Ifit rains tomorrow, then I will go to your house. …\GeoSec02_02.ppt

  5. If a sentence has noif-thenkey words, then use thesubjectof the sentence as the hypothesis and the object of the sentence as theconclusion. An example is; Babies are illogical. becomes; If a person is a baby, then that person is illogical. …\GeoSec02_02.ppt

  6. The converseof a statement is when you exchange the hypothesis and the conclusion in a statement. When pq, then theconverse is qp. Iftwo lines are perpendicular,thenthey intersect. and theconverseis Iftwo lines intersect,thenthey are perpendicular. Symbolically, pq(original), becomesqp …\GeoSec02_02.ppt

  7. Negation- The denial of a statement. The angle is obtuse. The denial of this statement is ; The angle is not obtuse. Other examples of mathematical statements and then their denial Symbolically, p (original), becomes p …\GeoSec02_02.ppt

  8. The inverseof a statement is formed by negating the hypothesis and the conclusion. Vertical angles are congruent. Iftwo angles are vertical, thenthey are congruent. and itsinverseis, Iftwo angles are NOT vertical, thenthey are NOT congruent. Symbolically,pq(original), becomespq …\GeoSec02_02.ppt

  9. Thecontrapositiveof a statement is formed by negating the hypothesis and the conclusion of the converse. original Iftwo lines are perpendicular, thenthey intersect. converse Iftwo lines intersect, thenthey are perpendicular. contrapositive Iftwo lines do not intersect, thenthey are not perpendicular. Symbolically,pq(original), becomesqp …\GeoSec02_02.ppt

  10. It can be proven that thecontrapositiveislogically equivalentto the original statement. A logically equivalentstatement has the form of pqqp or ifx2 > 4,thenx > 2 if(x > 2),then(x2 > 4) ifx 2,thenx2 4 if(3 = n + 1),thenn = 2 if(n=2),then(3 = n + 1) ifn 2,then3 n + 1 …\GeoSec02_02.ppt

  11. Ifyou are 13 years old, thenyou are a teenager. converse ** Ifyou are a teenager, thenyou are 13 years old. inverse ** Ifyou are NOT 13 years old, thenyou are NOT a teenager. contrapositive Ifyou are NOT a teenager, thenyou are NOT 13 years old. …\GeoSec02_02.ppt

  12. Ifan angle measures 90o, thenit is a right angle. converse Ifan angle is a right angle, thenit measures 90o. inverse Ifan angle is NOT a right angle, thenit does NOT measure 90o. contrapositive Ifan angle does NOT measure 90o, thenis NOT a right angle. …\GeoSec02_02.ppt

  13. Summary We converted written statements intoconditionals(if-thenstatements) in order to use logic to determine the validity (truth or falsehood) of those statements. The form of theif-thenisifp, thenq, orp q, where theif-partof the conditional is the hypothesis and thethen-partis the conclusion. We discussed theconverse, thenegation, theinverse, and thecontrapositiveof a conditional. We found that theinverseand theconverseof a true conditional, is not always itselftrue. We also discovered that the conditional and itscontrapositivearelogically equivalent. …\GeoSec02_02.ppt

  14. END OF LINE …\GeoSec02_02.ppt

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