WarmUp 1 2 3 Write in ifthen form

Warm-Up 1. 2. 3. Write in if-then form. An angle of 40 degrees is acute. Identify the hypothesis and conclusion. If it is Tuesday, then Phil plays tennis. Write the converse. Is the converse true or false? An angle that measures 120 degrees is obtuse.

Warm-Up continued 4. Write the inverse. Is it true or false? A triangle has 3 sides. 5. Write the contrapositive. Is it true or false? If aliens have visited Earth, then there is life on other planets. 6. 5 people have arrived at a meeting. Each one shakes hands one time with each of the others. How many different handshakes take place? Draw a diagram.

Activity: The original conjecture is underlined. Identify the converse, inverse, and contrapositive statement. n 1) I once knew a boy named Tyler who told his teacher, “All girls are afraid of spiders”. Boyce spoke up and said “I believe boys like spiders. ” Madison piped in “Kitty cats aren’t afraid of girls”. Caroline said “I think spiders are afraid of girls”.

2. 3 Deductive Reasoning n n n Deductive reasoning – uses a rule or facts to make a conclusion. Law of detachment - when a conditional is true and its hypothesis is true, we can assume the conclusion is true. Law of syllogism – if p then q is true and if q then r is true, then if p then r is true.

Deductive reasoning video

Law of Detachment Law of detachment: means to separate. n The law of detachment Takes an If -then statement (statement 1) and separates it into its parts to make steps 2 and 3. n

Law of Detachment n n n 1. If p then q. (Conjecture) 1. If Miss Kerr is happy then her students did their homework. 2. p is true 2. Miss Kerr is happy. 3. q is true. (Conclusion) 3. The class did their homework.

2. 3 Examples § 1) If a vehicle is a car, then it has 4 wheels. 2) A sedan is a car. 3) A sedan has 4 wheels. Use the law of detachment to form a conclusion.

GUIDED PRACTICE 1. If 90° < m R < 180°, then R is obtuse. The measure of R is 155°. Using the Law of Detachment, what statement can you make? ANSWER R is obtuse

Law of Syllogism n n Other isms - altruism, egotism, evangelism, fanaticism, feminism, idealism, imperialism, realism, and romanticism Syllogism could be seen as a principle of reasoning. A syllogist is someone who is skilled in eloquent words. Lawyers might be considered syllogists – connecting words with reasoning.

Law of Syllogism n n n 1. If p then q. (Conjecture) 1. If Derion gets his license then he can buy a car. 2. If q then r. (Connected conjecture) 2. If Derion buys a car then he will drive his friends to school. 3. If p then r. (Conclusion) 3. If Derion gets his license then he will drive his friends to school.

GUIDED PRACTICE 1. If Rachel takes Geometry this year, then she will take Algebra 2 next year. If Rachel takes Algebra 2 next year, then she will graduate. Using the Law of Syllogism, what statement can you make ? ANSWER If Rachel takes Geometry this year, then she will graduate.

Examples continued 1) If I watch TV, I will not do my homework. 2) I did my homework. Use law of detachment. n 1) If Tory takes the car to the store, then she will stop at the post office. 2) If Tory stops at the post office, then she will buy stamps. Use law of syllogism. n

GUIDED PRACTICE State the law of logic that is illustrated. 3. If you get an A or better on your math test, then you can go to the movies. If you go to the movies, then you can watch your favorite actor. If you get an A or better on your math test, then you can watch your favorite actor. ANSWER Law of Syllogism. 4. If x > 12, then x + 9 > 20. The value of x is 14 Therefore, x + 9 > 20 ANSWER Law of Detachment

2. 3 Group Activity n Create if-then statements to illustrate law of detachment and law of syllogism. Give to another student to apply the appropriate law.

Detachment 1. 2. 3. If p then q. p is true. q is true Syllogism 1. 2. 3. If p then q. If q then r. If p then r.

Warm-Up 1. 2. 3. Write the inverse of: Blondes have more fun. Write the converse of: Parallel lines never intersect. Write the contrapositive of: If two angles have a sum of 90˚, then the angles are complementary.

Answers 1. 2. 3. If you aren’t blonde then you don’t have more fun. If two lines never intersect then the lines are parallel. If 2 angles are not complementary then the sum of their measures is not 90˚.

Warm-Up Take the following Conjecture and create an illustration of a) the law of detachment and b) the law of syllogism. 1. If Tremaine presses Elmo’s foot then Tremaine and Elmo will do the chicken dance. n

Warm-Up: If a valid conclusion can be made write it and state the law used. 1. 2. 3. If you are a NJROTC cadet then you wear a uniform on Wednesday. Samaria is a cadet. Samaria wears a uniform on Wednesday. If Mario rips Jalista’s paper then she will get even. If Jalista gets even then she called the paper police. If Mario rips Jalista’s paper then she called the paper police.

Warm-Up continued 1. 2. 3. If Kayla is dancing then she made an A on her Geometry test. Kayla made an A on her Geometry test. No conclusion.

Warm-Up A. B. Identify the hypothesis and conclusion. Write the converse, inverse and contrapositive. 1. All children love lollipops.

If you are a child then you love lollipops. A. Hypothesis: you are a child Conclusion: you love lollipops B. Converse: If you love lollipops then you are a child. Inverse: If you are not a child then you don’t love lollipops. Contrapositive: If you don’t love lollipops then you are not a child.