Chapter 2.3 Conditional Statements Objective: Be able to recognize conditional statements and write converse, inverse and countrapositive statements Check.4.16 Use inductive reasoning to write conjectures and/or conditional statements Develop an understanding of the tools of logic and proof, including aspects of CLE 3108.4.3 formal logic as well as construction of proofs. Identify, write, and interpret conditional and bi-conditional statements along with Check.4.15 the converse, inverse, and contra-positive of a conditional statement. Conditional Statements - process If – then Hypothesis – Conclusion If you finish high school then you increase your lifetime earning potential by $1million If you finish college then you increase your lifetime earning potential by $3million Conditional Statements If – then Hypothesis – Conclusion If points A, B, and C lie on a line then they are collinear. An angle with a measure greater than 90 is an obtuse angle. Perpendicular lines intersect Two lines are perpendicular They intersect Conditional Statements – Truth? Statement – if you get 100%, then your teacher will give you an A TRUE If you get 100% correct, your teacher gives you an A. False If you get 100% correct, your teacher gives you a B. True, can’t say not You get 98%, your teacher gives you an A. You get 85% correct then your teacher gives you a B. True, can’t say not Conditional Statements Statement Statement Conditional Conditional Formed Formed by by Given hypothesis Given hypothesis and and conclusion conclusion Converse Converse Exchanging Exchanging hypothesis hypothesis and and conclusion conclusion Inverse Inverse Negate Negate both both hypothesis hypothesis and and conclusion conclusion Contrapositive Contrapositive Negate Negate both both hypothesis hypothesis and and conclusion of conclusion of converse converse Symbols Symbols pq pq qp qp ~p~q ~p~q ~q~p ~q~p Example Example If two angles angles have have the If two the same same measure measure they they are are congruent congruent If If two two angles angles are are congruent, congruent, then then they they have have the same measure the same measure If If two two angles angles do do not not have have the the same same measure, measure, then then they are not congruent they are not congruent If two angles are not congruent, then they do not have the same measure Conditional Statements Conditional Statement If two angles form a linear pair, then they are supplementary. Converse Statement Inverse Statement If two angles are supplementary, they form a linear pair FALSE If two angles do not form a linear pair, then they are not supplementary False Contrapositive If two angles are not supplementary, they do not form a linear pair. True Practice Assignment Page 111, 40 - 62 Even Check your practice Page 111, 40 - 62 Even 40. True 42. False 44. False 46. True 48. Converse: If a bird cannot fly, then it is an ostrich. false. Counterexample: The bird could be a penguin. Inverse: If a bird is not an ostrich, then it can fly. The inverse is false. Counterexample: The bird could be a penguin. Contrapositive: If a bird can fly, then the bird is not an ostrich; true. 50. If a figure is a rectangle, then it is a square. false. If a figure is not a square, false. If a figure is not a rectangle, then it is not a square. true. then it is not a rectangle. 54. Converse true 56. Contrapositive False 60. False 62.