Download Deductive Reasoning Law of Detachment Law of Syllogism:

Deductive Reasoning Notes & Practice
Geometry
Vocabulary
Deductive
Reasoning
Law of
Detachment
Definition
Using facts, definitions and logic to
form a logical argument
If the hypothesis of a true
conditional is true, then the
conclusion is true.
If p → q repeat
conclude q
Law of
Syllogism:
p then you can
Two or more conditionals, use like
transitive property
If p → q If q → r conclude p → r
N_____________________
D_____________ B_______
Example
If two angles are adjacent and supplementary
then they form a line. (Use definition of linear
pair)
If it is the weekend then Bruce will go to the
movies. It is Saturday.
Conclusion: __Bruce will go to the
movies_______
If I walk to the store then I will go get ice cream. If
I go get ice cream then I will spend all my money.
Conclusion: If I walk to the store I will spend all
my money.
Examples:
1. Use Law of Detachment to make a valid conclusion if the situation is true.
a. If two angles have the same measure, then they are congruent. You know that m  A = m  B.
A ≅  B
b. Jesse goes to the gym every weekday. Today is Monday.
Not possible.
2. If possible, use the Law of Syllogism to write the conditional statement that follows from the pair of
true statements.
a. If Ron eats lunch today, then he will eat a sandwich. If Ron eats a sandwich, then he will drink a
glass of milk.
If Ron eats lunch today then he will drink a glass of milk.
b. If x>6 then x2 > 36. If x2 >25, then x >5.
Not possible
c. If a triangle is equilateral, then all of its sides are congruent. If a triangle is equilateral, then all the
angles in the interior of the triangle are congruent.
Not possible
3. What conclusion can you make about the addition of an odd integer and an odd integer?
If you add an odd integer with an odd integer then your sum is an even integer.
4. Tell whether the statement is a result of inductive or deductive logic
and explain your reasoning.
a. The runners average speed decreases as time spent running
increases.
Deductive – based on the graph
b. The runners’ average speed is slower when running for 40
minutes than when running 10 minutes.
Inductive – based on a specific example
Practice: State the law of logic (Law of Detachment or Law of Syllogism) that is illustrated below.
1. A. If you take Geometry then you do not take Algebra. You are in Mrs. Frye’s Geometry class. You
don’t take Algebra.
B.
If the Redskins win tonight then my team gets 20 points. If my team gets 20 points then I will be in
first place. The Redskins won their game tonight and my team is in first place.
Decide if either law of logic is used for each example. If not, write not valid. If valid, state the law
(Detachment or Syllogism) used and then write a valid statement that would follow.
1. If 0 < m  A < 90 , then  A is acute. The measure of  A is 38 .
2. If there is a nice breeze, then the mast is up. If the mast is up, then we will sail to Dunkirk.
3. If you do your homework, then you can watch TV. If you watch TV then you can watch your favorite
show.
4.
If Chess Club meets today, then it is Thursday. Today is Thursday.
5. If it is snowing, then school is closed. It is snowing today.
6. If I drive to the left then I will miss the sand trap. If I miss the sand trap then I will be on the green. If I am
on the green then I am ready to putt.
______________________________________________________________________________________
7. Use inductive reasoning to make a conjecture about the sum of a negative integer and itself. Then use
deductive reasoning to show the conjecture is true.
Use the Law of Syllogism, if possible, to solve the following.
9. If x→~ w, ~ w →y , y → z , then x→__ ___.
10. If a→b , b → f , f→g , ~g→~ h , then a→_ ____.