Name: ____________________
Hour: _____ Date: ___/___/___
Geometry – Venn Diagrams
In Agatha Christie’s “Murder on the Orient Express” a murder has occurred. One scenario is
that the conductor, who left the train because the train is stuck in a snow bank, is the murderer.
The detective is logically trying to solve the murder. He uses a crushed watch to determine the
time of death. Therefore, the detective says “If the crime was committed at a quarter past one,
then the murderer could not have left the train.”
The detective’s statement is an example of a conditional statement, where the “if” part is the
hypothesis and the “then” part is the conclusion. A conditional statement can be represented
symbolically by a → b read as “If a, then b.”
In the Murder on the Orient Express, a represents the words “the crime was committed at a
quarter past one” and b represents the words “the murderer could not have left the train.”
This situation can also be modeled using Venn diagrams where the inner circle represents the “a”
part of the conditional statement, and the outer circle represents the “b” part of the conditional
statement.
A
The murderer
could not have
left the train
B
The crime was
committed at
quarter past one
1. If a flag is the current United States Flag, then it has 50 stars on it.
a. Create a Venn diagram for this situation.
b. What is the hypothesis of this conditional situation?
c. What is the conclusion of this conditional situation?
2. Write a conditional statement for this situation.
a. What is the hypothesis of this conditional situation?
b. What is the conclusion of this conditional situation?
You are in
Michigan
You are
crossing the
Mackinac
Bridge
3. Two angles whose sum is 1800 are supplementary.
a. Write a conditional statement for this situation.
b. Create a Venn diagram for your conditional statement from part a.
c. What is the hypothesis of this conditional situation?
d. What is the conclusion of this conditional situation?
4. Given this statement: All Detroit Red Wings players make a lot of money. Which of the
following statements are supported by this statement? Explain your answer.
a. If you are a Detroit Red Wing player, then you make a lot of money.
b. If you make a lot of money, then you are a Detroit Red Wing player.
5. A right angle measures 900. Which of the following statements are supported by this
statement? Explain your answer.
a. If an angle is a right angle, then it measures 900.
b. If an angle measures 900, then it is a right angle.