LOGIC. 11 Converse, Inverse, Contrapositve. 12/13 Quiz Biconditional Statements
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1 Name Period GP LOGIC I can define, identify and illustrate the following terms Conditional Statement Hypothesis Conclusion Inductive Reasoning Deductive Reasoning Inverse Converse Contrapositive Biconditional Truth Value Negation Counterexample Logically Equivalent Conjecture Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday 10 Inductive Reasoning and Conditional Statements 17 Review 11 Converse, Inverse, Contrapositve 18 TEST 2 12/13 Quiz Biconditional Statements 14 Deductive Reasoning Monday, 9/10 (2-1 and 2-2) Inductive Reasoning and Conditional Statements I can use inductive reasoning to identify patterns and make conjectures I can determine the hypothesis and conclusion of a conditional statement. I can write a conditional statement from a sentence. ASSIGNMENT: pg. 77 (11-13, 16, 20-23, 28,31) pg (13-18) Tuesday, 9/11 (2-1 and 2-2) Inductive Reasoning and Conditional Statements I can determine the truth value of a conditional statement. I can give prove a conditional statement false by giving a counterexample. I can write the inverse, converse, and contrapositive of a conditional statement. ASSIGNMENT: pg. 77 (8, 10, 25, 37, 38) pg (10-12, 22, 38, 42-44, 50-52) Wednesday, 9/12 and Thursday, 9/13 Quiz: Inductive Reasoning and Conditional Statements (2-4) Biconditional Statements Determine the logical equivalence of a set of conditional statements. I can write a biconditional statement. I can write a biconditional statement as 2 conditional statements. I can convert to and from definitions and biconditional statements. I can determine the truth value of a biconditional statement. ASSIGNMENT: pg. 99(10, 13, 16-19, 20-23, 38, 41, 52-53) Friday, 9/14 (2-3) Deductive Reasoning and Verify Conjectures I can apply the Law of Syllogism and the Law of Detachment in logical reasoning. ASSIGNMENT: pg. 91 (1, 4-12, 15-18, 23)
2 Monday, 9/17 I can review for the test in class. ASSIGNMENT: Review Assignment Review Tuesday, 9/18 Test 2 Logic I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material. ASSIGNMENT: Test #2 Grade:
3 TERM: Conditional Statement Hypothesis Conclusion NOTES: Conditional Statements A statement written in if-then format The phrase following but NOT INCLUDING the word if. The phrase following but NOT INCLUDING the word then. Ex 1: Underline the hypothesis and circle the conclusion of the conditional statement below. If you have an 85% or higher, then you do not need to retest. Ex 2: Rewrite the statement below as a conditional statement, underline the hypothesis and circle the conclusion of the conditional statement below. Conditional: A car with poor brakes is a menace on the highway. Ex 3: Rewrite the statement below as a conditional statement, underline the hypothesis and circle the conclusion of the conditional statement below. Geometry teachers give their students homework on days that end in y. Conditional: TERM: Negation Inverse The denial of a statement (add not) Formed by negating both the hypothesis and conclusion of a conditional statement (add not) Ex 6: Write the inverse of the conditional statement below. If you pass the TAKS test, then you will graduate. Inverse: Ex 7: Write the inverse of the following statement. If school is in session, then it is a weekday. Inverse:
4 TERM: Converse Formed by switching the hypothesis and conclusion of a conditional Ex 4: State the converse of the conditional statement. Converse: If it is Saturday, then you do not have school. Ex 5: Write the converse of the conditional statement below. Converse: If an angle has a measure of 120, then it is an obtuse angle. TERM: Contrapositive Ex 8: Write both the converse and the contrapositive of the conditional statement below. Formed by negating the hypothesis and conclusion of the converse. (switch and add not) If you run a red light, then you are breaking a traffic law. Contrapositive: Ex 9: Write the contrapositive of the conditional statement below. Contrapositive: If you leave the classroom, then you must take a pass with you. TERM: Counterexample An example that follows the hypothesis, but not the conclusion. Ex 10: Give a counterexample for the statement. If you leave the classroom, then you must take a pass with you. Counterexample:
5 Biconditional Statements Example: Conditional: If a solution has a ph less than 7, then it is an acid. Converse: If a solution is an acid, than its ph is less than 7. Biconditional: A solution is an acid if and only if it has a ph less than 7. Your Turn: 1) Conditional: If a point is a midpoint, then it divides a segment into two congruent segments. Converse: Biconditional: if and only if II. Good definitions are also true when read forwards and backwards. Therefore, we also write as biconditional statements. Example: Defintion: A triangle is a three-sided polygon. Biconditional: A figure is a triangle if and only if it is a three-sided polygon. Your Turn: 1) Definition: A straight angle is an angle whose measure is 180. Biconditional: 3) Definition: An angle is obtuse when it measures between 90 and 180. Biconditional:
6 III. Now, write the conditional statement and the converse from the following biconditional statement. Biconditional: Two angles are congruent if and only if their measures are equal. Conditional: Converse: Multiple Choice: 1. Which of the following biconditionals is equivalent to the definition: An endpoint is a point at the end of a segment or at the start of a ray. a. A point is an endpoint if and only if it is the start of a ray. b. A point is an endpoint if and only if it lies on a segment or a ray. c. A point is an endpoint if an only if it is a point. d. A point is an endpoint if and only if it is at the end of a segment or the start of a ray. 3. Which of the following could be a conditional statement for the following biconditional? You can get your license if and only if you passed the drivers test. a. If you take the drivers test, then you will get your license. b. If you passed the drivers test, then you can get your license. c. If you can get your license, then you passed the drivers test. d. All of the above could be conditional statements. Truth Values For a biconditional to be true, both the and the must be true. If it is false, then you give a counterexample. Ex. A rectangle has side lengths of 12 cm and 25 cm if and only if its area is 300 cm2. Conditional. Converse:. Conditional truth value: Converse truth value:
7 Ex. A natural number n is odd n2 is odd. Conditional. Converse:. Conditional truth value: Converse truth value: Law of Syllogism/Detachment Use the Law of Syllogism (Transitive property) and the Law of Detachment to determine the logical conclusion for each of the following. If the statements do not follow either pattern, write no valid conclusion. Law of Syllogism (transitive property) p q q r r s Therefore, p s Law of Detachment p q p is true therefore, q is true 1. If 2x + 3 = 17, then x = 7 2x + 3 = 17 Conclusion: 2. If Joan goes out with David, then she will watch a movie Saturday night. Joan watched a movie Saturday night. Conclusion : 3. If I go on vacation, I ll spend money. If I spend money, I ll be broke. If I m broke, I ll have to get another job. Conclusion: 4. If Paul divorces Veronica, then he will not receive his inheritance. Paul divorces Veronica. Conclusion: 5. If I pass geometry, I won t have to go to summer school. If I don t go to summer school, I ll get a job. If I get a job, I ll make money. Conclusion: 6. If ABCD is a rectangle, then the diagonals are congruent. The diagonals are congruent. Conclusion: 7. If it s sunny Saturday, then I ll go to the beach. If I go to the beach, then I ll lay in the sun. If I lay in the sun, I ll get a sunburn. Conclusion:
8 8. If you use Shining Smile toothpaste, then you will be popular. You are popular. Conclusion : 9. If Chris is a sophomore, he takes English II. Chris is a sophomore. Conclusion: 10. If the treasure is discovered, then pirate Jack will walk the plank. The treasure is discovered. Conclusion: 11. If I don t wear a sweater, I ll get cold. If I get cold, I ll get sick. If I get sick, I ll miss the dance. Conclusion: 12. If 1 and 2 are vertical angles, then they are equal. 1 and 2 are equal. Conclusion: 13. If 2 angles are linear, then they are supplementary. If 2 angles are supplementary, then their sum is 180º. Conclusion: 14. If Linda takes the bus, she ll be on time for work. Linda takes the bus. Conclusion: 15. If Hemlock Bones decodes the secret message, then the agent will live. The agent lives. Conclusion: 16. If Mr. Jones gets home on time, then he and Mrs. Jones will attend a meeting. If Mr. and Mrs. Jones attend a meeting, then Lisa will visit grandma. If Lisa visits grandman, then she will practice the piano. If Lisa practices the piano, then she will go to bed late. Conclusion: 17. If Anakin goes to the dark side, then he will become Darth Vadar. If he becomes Darth Vadar, then he will wear a black mask. Conclusion: 18. If Karen goes to Starbucks, then she will buy a Decaf. Mocha. Karen buys a Decaf. Mocha. Conclusion: 19. If Ethan is passing all of his classes, then he gets to go to the movies. Ethan is passing all of his classes. Conclusion:
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