Lesson 2-4: Deductive Reasoning
NAME______3.Nov.15
Scaffolding Questions
What other evidence might a detective collect?
Why is eliminating suspects useful for detectives?
What could be some limitations to using fingerprints as evidence?
Define inductive reasoning: ______
Define deductive reasoning:
______
______
Law of Detachment
- Determine whether each conclusion is based on inductive or deductive reasoning.
- In Miguel's town, the month of April has had the most rain for the past 5 years. He thinks that April will have the most rain this year.
- Sandra learned that if it is cloudy at night it will not be as cold in the morning as it would be if there are no clouds at night. Sandra knows it will be cloudy tonight, so she believes it will not be cold tomorrow morning.
Lesson 2-4: Deductive Reasoning
NAME______3.Nov.15
- Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.
Given: If a figure is a square, then it is a parallelogram.
Conclusion: The figure is a square.
- Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning using a Venn diagram.
Given: If a triangle is equilateral, then it is an acute triangle.
Conclusion: The triangle is acute.
Law of Syllogism
- Determine which statement follows logically from the given statements.
(1) If Jamal finishes his homework, he will go out with his friends.
(2) If Jamal goes out with his friends, he will go to the movies.
A. If Jamal goes out with his friends, then he finishes his homework.
B. If Jamal finishes his homework; he will go to the movies.
C. If Jamal does not go to the movies; he does not go out with his friends.
D. There is no valid conclusion.
- Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no conclusion and explain your reasoning.
Given: If it snows more than 5 inches, school will be closed.
Conclusion: It snows 7 inches.
Lesson 2-4: Deductive Reasoning
NAME______3.Nov.15
EXERCISES
- Inductive and Deductive Reasoning
Determine whether each conclusion is based on inductive or deductive reasoning.
a.Every time Kennedy has skipped studying for a science test, she has gotten at least six wrong. Kennedy skipped studying for her science test today, so she concludes that she will get at least six wrong.
b.If Cale is late enrolling for summer school, he will be assessed a late fee of $30. Cale's enrolled late this summer, so he concludes that he will be assessed a late fee of $30.
- Use the Law of Detachment
Determine whether each conclusion is valid based on the given information. If not, write invalid.Explain your reasoning.
a. Given: If a point is a midpoint of a segment, then it divides thesegment into two congruent segments.
Conclusion: W is the midpoint of .
b.Given: If Rosario goes to the gym, he will wear athletic socks.
Rosario is wearing athletic socks.
Conclusion: Rosario is at the gym.
Lesson 2-4: Deductive Reasoning
NAME______3.Nov.15
- Judge Conclusions Using Venn Diagrams
Determine whether each conclusion is valid based on the given information. If not, write invalid.Explain your reasoning using a Venn diagram.
Given: If a boy is in choir, then he is not in band.
Kyle is a boy who is not in band.
Conclusion: Kyle is in choir.
- Standardized Test Practice
Determine which statement follows logically from the given statements.
(1)If a figure is a square, then it has four right angles.
(2)If a figure has four right angles, then it is a rectangle.
A. If a figure has four right angles, then it is a square.
B. If a figure is a square, then it has four right angles.
C. If a figure is a square, then it is a rectangle.
D. There is no valid conclusion.
- Apply Laws of Deductive Reasoning
Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.
Given: (1) If two angles form a linear pair, then they are supplementary.
(2) If two angles are supplementary, then the sum of the angles equals 180.