• Use the Law of Detachment.

• Use the Law of Syllogism.

Lesson 2-3: Deductive Reasoning

TARGETS

LESSON 2-4: Deductive Reasoning

Have you ever tried to convince someone of something using

facts and arguments?

Deductive Reasoning!!!!!!

LESSON 2-4: Deductive Reasoning

Deductive Reasoning

Uses facts, rules, definitions, or properties to reach logical conclusions

**It is very important not to assume anything more than** exactly what is written

Inductive and Deductive Reasoning

A. 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.

EXAMPLE 1

LESSON 2-4: Deductive Reasoning

Determine whether the conclusion is based on inductive or deductive reasoning.

B. Sandra learned that if it is cloudy at night it will not be as cold in the morning than if there are no clouds at night. Sandra knows it will be cloudy tonight, so she believes it will not be cold tomorrow morning.

Inductive and Deductive Reasoning

C. 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.

EXAMPLE 1

LESSON 2-4: Deductive Reasoning

Determine whether the conclusion is based on inductive or deductive reasoning.

D. If Cale is late enrolloing for summer school, he will be assessed a late fee of $30. Cale has enrolled late this summer, so he concludes that he will be assessed a late fee of $30.

Use the Law of Detachment

Determine whether the 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 the segment into 2 congruent segments.

• W is the midpoint of DC.

Conclusion:

LESSON 2-4: Deductive Reasoning

EXAMPLE 2

€

DW ≅WC

Use the Law of Detachment

Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.

B.Given: • If Billy goes to the gym, he will wear athletic socks..

• Billy is wearing athletic socks.

Conclusion: Billy is at the gym.

LESSON 2-4: Deductive Reasoning

EXAMPLE 2

Judge Conclusions Using Venn Diagrams

Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning using a Venn diagram.

A.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.

LESSON 2-4: Deductive Reasoning

EXAMPLE 3

Judge Conclusions Using Venn Diagrams

Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning using a Venn diagram.

B.Given: • If a triangle is equilateral, then it is an acute

triangle. • The triangle is equilateral.

Conclusion: The triangle is acute.

LESSON 2-4: Deductive Reasoning

EXAMPLE 3

Use the Law of Syllogism

Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements.

A.(1) If a figure is a square, then it has four right right angles.(2) Figure with four right angles is a rectangle.

LESSON 2-4: Deductive Reasoning

EXAMPLE 4

Use the Law of Syllogism

Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements.

B.(1) Perpendicular lines form right angles.(2) The sum of complementary angles equals 90.

LESSON 2-4: Deductive Reasoning

EXAMPLE 4

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 conclusion and explain your reasoning.

LESSON 2-4: Deductive Reasoning

EXAMPLE 5

Given: If it snows more than 5 inches, school will be closed. It snows 7 inches.

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.

LESSON 2-4: Deductive Reasoning

EXAMPLE 5

Given: (1) If 2 angles form of a linear pair, then they are supplementary. (2) If 2 angles are supplementary, then the sum of the

angles equals 180.