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1 Notes Conditional Statements and Logic.notebook August 10, 2016 Conditional Statements and Inductive vs. Deductive Reasoning Cobb Honors Standards 2.1 Use conjecture, inductive & deductive reasoning, counter examples, and informal proofs to justify mathematical arguments. Aug 93:17 PM What am I learning today? How to write conditional statements and evaluate using inductive and deductive reasoning How will I show that I learned it? Evaluate the validity of conditional statements and their converses, inverses, and contrapositives. Aug 93:18 PM 1 1 Notes Conditional Statements and Logic.notebook August 10, 2016 What is a conditional statement? An "if then" statement where the "if" part is the hypothesis and the "then" part is the conclusion. Notation: p = hypothesis q = conclusion Aug 93:24 PM Identify the hypothesis and conclusion in the following conditional statement. If it is raining this afternoon, then band practice will be held inside. Hypothesis: Conclusion: Aug 93:26 PM 2 1 Notes Conditional Statements and Logic.notebook August 10, 2016 Rewrite the following statement as a conditional statement if "if then" form. You may need to add or subtract words. All triangles have 3 sides. Conditional Statement (p ⇒ q): Aug 93:26 PM Converse: take the conditional statement and SWITCH the hypothesis and conclusion. (think of a con-artist who switches things) Find the converse of your conditional statement If a polygon has 3 sides, then it is a triangle. Converse Statement (q ⇒ p): Aug 93:26 PM 3 1 Notes Conditional Statements and Logic.notebook August 10, 2016 Inverse: take the conditional statement and NEGATE the hypothesis and conclusion. (think opposite) Find the inverse of your conditional statement If a polygon has 3 sides, then it is a triangle. Inverse Statement (~p ⇒ ~q): Aug 93:26 PM Contrapositive: take the conditional statement and SWITCH and NEGATE the hypothesis and conclusion. Find the contrapositive of your conditional statement If a polygon has 3 sides, then it is a triangle. Contrapositive Statement (~q ⇒ ~p): Aug 93:26 PM 4 1 Notes Conditional Statements and Logic.notebook August 10, 2016 A counterexample is one example that can prove an entire statement false. Example: If a number is prime, then it is an odd number. Counterexample: Aug 93:32 PM 1) For the following conditional statement, find the converse, inverse, and contrapositive. 2) Then, state if each statement is true or false. 3) If a statement is false, provide a counterexample. "If an angle measures 100o, then it is an obtuse angle." Converse: Inverse: Contrapositive: Aug 93:45 PM 5 1 Notes Conditional Statements and Logic.notebook August 10, 2016 Inductive Reasoning Inductive Reasoning specific to general. Based on evidence, generalize a conclusion to encompass all similar cases. Example: Physically reflect A(3, 5) & B(2, 3) across the xaxis and get A'(3, 5) & B(2, 3). Conclude that reflecting across the xaxis changes the sign of y. Aug 93:49 PM Deductive Reasoning Deductive Reasoning general to specific. Based on evidence and using definitions, theorems, and postulates, conclusion on result of specific case. Example: Definition of perpendicular lines as intersecting at right angles. Definition of right angles as measuring 90o. Given two lines that intersect to make a 90o angle, conclude that the lines are perpendicular to one another. Aug 93:49 PM 6 1 Notes Conditional Statements and Logic.notebook August 10, 2016 Homework: In the Textbook p. 25, #14, 15, 17, 18, 2027, 37, 38, 40 p. 33, #1329, 38, 40, 41 p. 39, #23, 910 Aug 108:12 AM 7