2.1 Inductive Reasoning & Conjecture2.2 Logic2.3 Conditional Statements

2-4 Deductive Reasoning

Honors Geometry

Main Ideas

Use the Law of Detachment

Use the Law of Syllogism

Vocabulary

Deductive Reasoning uses facts, rules, definitions, or properties to reach logical conclusions.

Law of Detachment: If p → q is true and p is true then q is also true.

Law of Syllogism: If p → q and q → r is true, then p → r is true.

Law of Detachment

If p → q is true and p is true then q is also true

If you are a CD teacher, then you have an in-service

on September 25th.

Given: Mrs. Bayer is a CD teacher.

Conclusion:

Law of Detachment

If p → q is true and p is true then q is also true

If you are a CD teacher, then you have an in-service

on September 25th.

Given: Mrs. Bayer is a CD teacher.

Conclusion: Mrs. Bayer has an in-service on September 25th.

Ex 1:

Using Law of Detachment, come up with conclusions for the following:

1. The football team has a game on Friday.

2. Paul is a member of the football team.

3.

1. All cars have 4 wheels

2. A Honda CR-V is a car.

3.

Ex 1:

Using Law of Detachment, come up with conclusions for the following:

1. The football team has a game on Friday.

2. Paul is a member of the football team.

3. Paul has a football game on Friday.

1. All cars have 4 wheels

2. A Honda CR-V is a car.

3.

Ex 1:

Using Law of Detachment, come up with conclusions for the following:

1. The football team has a game on Friday.

2. Paul is a member of the football team.

3. Paul has a football game on Friday.

1. All cars have 4 wheels

2. A Honda CR-V is a car.

3. A Honda CR-V has 4 wheels.

Law of Syllogism

If p → q and q → r is true, then p → r is true.

1. If you wear yoga pants and violate the dress code you will need to go to the office.

2. If you go to the office you will need to change your clothes.

3. If you wear yoga pants and violate the dress code you will need to change your clothes.

Law of Syllogism

If p → q and q → r is true, then p → r is true.

1. If you wear yoga pants and violate the dress code, then you will need to go to the office.

2. If you go to the office you will need to change your clothes.

3. If you wear yoga pants and violate the dress code you will need to change your clothes.

Law of Syllogism

If p → q and q → r is true, then p → r is true.

1. If you wear yoga pants and violate the dress code, then you will need to go to the office.

2. If you go to the office then you will need to change your clothes.

3. If you wear yoga pants and violate the dress code you will need to change your clothes.

Law of Syllogism

If p → q and q → r is true, then p → r is true.

1. If you wear yoga pants and violate the dress code, then you will need to go to the office.

2. If you go to the office then you will need to change your clothes.

3. If you wear yoga pants and violate the dress code then you will need to change your clothes.

Ex last one:

Using Law of Syllogism, come up with a valid conclusion for the following:

1. If you attend CDHS then your mascot is the ram.

2. If your mascot is the ram, then your colors are green and white.

3.

1. Perpendicular lines make right angles.

2. All right angles equal 90˚.

3.

Ex last one:

Using Law of Syllogism, come up with a valid conclusion for the following:

1. If you attend CDHS then your mascot is the ram.

2. If your mascot is the ram, then your colors are green and white.

3. If you attend CDHS, then your colors are green and white.

1. Perpendicular lines make right angles.

2. All right angles equal 90˚.

3.

Ex last one:

Using Law of Syllogism, come up with a valid conclusion for the following:

1. If you attend CDHS then your mascot is the ram.

2. If your mascot is the ram, then your colors are green and white.

3. If you attend CDHS, then your colors are green and white.

1. Perpendicular lines make right angles.

2. All right angles equal 90˚.

3. Perpendicular lines create 90º angles.

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