Deductive Reasoning: Law of Detachment/ Logic Puzzles

2.3 Deductive Reasoning
Prentice Hall Geometry: Page 94- 96
Objective: Students will use the Law of Detachment and the Law of Syllogism.

Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

An auto mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins work on a car and finds the battery is dead. What conclusion will she make?
The mechanic can conclude that the car will not start.

Law of Detachment
If a conditional is true and its hypothesis is true, then its conclusion is true.
If P Q is a true statement and p is true, then q is true.

If there is lightning, then it is not safe to be out in the open. Marla sees lightning from the soccer field.
It is not safe for Marla to be out in the open.

If it is snowing, then the temperature is less than or equal to 32˚F.
The temperature is 20˚F.
It is not possible to conclude that it is snowing.

Law of Detachment
If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Brent is a pitcher. On Monday, he pitches a complete game. What can you conclude?

Brent should not pitch a complete game on Tuesday.

If M is the midpoint of a segment, then it divides the segment into two congruent segments.
M is the midpoint of .
By Law of Detachment, you can conclude that M divides into two congruent segments, or

If an angle is obtuse, then it is not acute.
is not obtuse.
It is not possible to conclude that is acute.

If a road is icy, then driving conditions are hazardous.
Driving conditions are hazardous.
It is not possible to conclude that it is icy.

bulbs
There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

Answer
Turn one light switch one.
Wait about 20 minutes, then turn it off.
Turn another light on, and proceed upstairs.
One light should be on,
Two lights are off- however, one light is hot and one is cold.

apartment
A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment. Can you explain why?

Answer
The man is a little person.
On rainy days, he has an umbrella to push button ten.
When others are in the elevator, he gets them to push button ten.
Otherwise, he can only reach 7.