Conditional Statements 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 CLE 3108.4.3 Develop an understanding of the tools of logic and proof, including aspects of formal logic as well as construction of proofs. Check.4.15 Identify, write, and interpret conditional and bi-conditional statements along with 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 If you get 100% correct, your teacher gives you an A. If you get 100% correct, your teacher gives you a B. You get 98%, your teacher gives you an A. You get 85% correct then your teacher gives you a B. TRUE False True, can’t say not True, can’t say not
Conditional Statements Formed by Symbols Example Conditional Given hypothesis and conclusion pq If two angles have the same measure they are congruent Converse Exchanging hypothesis and conclusion qp If two angles are congruent, then they have the same measure Inverse Negate both hypothesis and conclusion ~p~q If two angles do not have the same measure, then they are not congruent Contrapositive Negate both hypothesis and conclusion of converse ~q~p If two angles are not congruent, then they do not have the same measure Statement Formed by Symbols Example Conditional Given hypothesis and conclusion pq If two angles have the same measure they are congruent Converse Exchanging hypothesis and conclusion qp If two angles are congruent, then they have the same measure Inverse Negate both hypothesis and conclusion ~p~q If two angles do not have the same measure, then they are not congruent Contrapositive Negate both hypothesis and conclusion of converse ~q~p Statement Formed by Symbols Example Conditional Given hypothesis and conclusion pq If two angles have the same measure they are congruent Converse Exchanging hypothesis and conclusion qp If two angles are congruent, then they have the same measure Inverse Negate both hypothesis and conclusion ~p~q Contrapositive Negate both hypothesis and conclusion of converse ~q~p Statement Formed by Symbols Example Conditional Given hypothesis and conclusion pq If two angles have the same measure they are congruent Converse Exchanging hypothesis and conclusion qp Inverse Negate both hypothesis and conclusion ~p~q Contrapositive Negate both hypothesis and conclusion of converse ~q~p
Conditional Statements If two angles form a linear pair, then they are supplementary. Converse Statement If two angles are supplementary, they form a linear pair FALSE Inverse Statement 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 50. If a figure is a rectangle, then it is a square. false. If a figure is not a square, then it is not a rectangle. false. If a figure is not a rectangle, then it is not a square. true. 54. Converse true 56. Contrapositive False 60. False 62. 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.